There's a pretty good chance that reason is more concept than simplicity - it's the closest fit for a lot of the heroes in the adjacent literature. It might well be the closest fit for the vast majority.
While my favoured edition is not 5e, I can provide an answer in the spirit of what 5e tried to accomplish, which is being recognisably DnD while attempting to be more of a gateway game that fits the middleweight category. So:
- Bring back 4e power formatting, because natural language is awful
- Similarly, bring back 4e monster statting
- Ditch alignment entirely. Encourage GMs to track "faction reputations" instead.
- Measure things in range bands rather than feet, so that the game can stop lying about supporting theatre of the mind and actually do it.
- Make sure the 'default' subclasses/variants of all classes are of roughly equal complexity. Demanding a 'simple' class for dumb players is dumb - designers shouldn't have to cater for people that don't actually want to play the game.
- In fact, make very clear that the game has been playtested well, and should work well with zero houserules. Present rules changes as "tweaks for your group". Design the game with the assumption that every rule will be used and followed to the letter.
- Every level should bring with it an interesting mechanical decision - which may require cutting down the total number of levels
- Going back to classes, make sure all classes have narrative power. This doesn't mean "narrative mechanics"; it means that if a wizard can cast charm person and It Just Works, then the rogue should be able to use Steal Heart and It Just Works - no adjudication required, any more than Charm Person requires.
- Figure out some way to make ability scores entirely vestigial behind-the-scenes, such that 'charisma Fighter' is a valid and mechanically powerful character.
I feel like this one is closest to what I'd aim for, and will use it as a basis for my answer:
So, in order:
- Partially bring back 4e power formatting. Make the entries look like pages from a spellbook, however; this aesthetic is essential. Choose colours, fonts, etcetera with this in mind. Natural language is pretty awful, but if we don't want 7e to undo all the good my reign of terror will inflict we need to make sure our consistent templates read flavourfully. More flavour text and more effort put into it please (and let's include more details on stuff like spell components while we're at it).
- 4e monster design OTOH, yeah let's do this.
- Alignment can't go. It's iconic IP. Instead, let's just tighten it up. Make it something like "PCs are generally expected to pick a Good Alignment; non-heroic PCs may be allowed at DM's discretion". Clarify/redefine Lawful/Chaotic as Has A Code vs. Has A Heart, and clarify/redefine Good/Evil as The Good Of The Many vs. The Good of The Me.
- Dual design for range approximations and precise measurements; using feet is fine. That is to say, instead of "Shift 1" or "5 foot step" stick with "disengage" and other non-numerical terms so that there be a section on "gridded combat" and another on "Theatre of the Mind" and they just redefine a few key terms. Similarly use descriptive terms for size and distance; e.g. Longbows have a range of "long" which is defined in the gridded combat section as 150 feet and in the ToTM as "long".
- Put a "simplified" version of every class right there in the first PHB. There's a niche, cater. Don't leave anyone out in the cold.
- Yeah, make it clear the game is designed to work as written.
- Levels don't need to specifically come with interesting decisions. Why? Because respeccing is fun. If you can change your spell load-out every long rest, characters should hopefully avoid being boring. Note: Simplified Wizard (etc) can't do this, because they're Simplified. In fact, Simplified Classes pretty much just make one decision at level one and then keep merrily leveling up without any further need for player input. (e.g. Simplified Necromancer has pre-set spells, abilities, etc. all calibrated to make them feel Necromancer-y. No customization unless playtests disprove my theories.)
- All classes get narrative power, "mundane" classes get it hidden in the skill rules by giving them access to narrative-level skills. So Bluff Proficiency lets you try to fast talk them, Bluff Mastery lets you fast talk them.
- Decouple stats from class features (and "attack bonus", "HP" and "AC" count as class features), but give stats things they do independent of class.
Keep: Short list of chunky feats, Advantage, bounded values (actually let's do those better).
- Make magic items more exciting. No, +1 isn't good enough anymore. Probably implement some kind of "Build the Legend" whereby it becomes more badass as you do, rather than always having to find better loot. In fact, make "quest for it" what *makes* legendary items powerful; you can't just hand someone a Holy Avenger, they have to earn it (and there's rules for that) or it's just a sword in their hands.
...I actually like 5e, at least the way it's written (I've played very little actual D&D). So if someone asked me to help design 6e, and for some reason wouldn't listen if I said "stop being greedy and making people buy a completely new edition every 5 years," I'd start with 5e as a base, with not toooooo much modding:
- Goblins/orcs, gnolls, and lizardpeople get to be playable races, are not always evil, and do not have a penalty to intelligence. Who are you trying to sell the game to, KKK members?
- Skills get more meat back on them, as in d20 Modern. These include weapon and non-weapon skills, and weapon skills are reduced to around 7 to 10 classes ("sword," "axe," etc.), with a total of maybe 20-25 unique weapons. You don't need 2349062057.3 different polearms.
- The equipment and labor cost table gets a review by someone with background in economic history. No, a skilled worker does not make 10 times as much money as an unskilled one - try 2 times. You can tell surprisingly good stories using realistic economic history, boiling down to "go out and earn money so that you don't have to live in near-poverty for your entire life."
- The spell list gets streamlined even further. There was no need for five different Bigby's Hand spells and it's good they got consolidated to one, but there's still work to do. For one, cut down the different lists to 2, arcane and divine, as in 2e, and use spheres to differentiate clerics from druids.
- Advantage and disadvantage stay. Optionally the reroll feature gets converted to an equivalent bonus or penalty, which is about +3/-3, just to cut down on the number of rolls required.
Just give us Orcs as a playable race for god's sake!
Give the public what they want. Leave Half Orcs as well if necessary (or remove them - whatever). People want to play Orcs, and they just don't work as always evil antagonists: (leaving aside any ethical or political considerations around the topic) they simply aren't scary any more.
For classes: I'd rework Sorcerer from scratch, fix the ranger, oomph the champion.
Re-do the weapons table entirely.
I get that wizards are less quadratic and have more to do now, but magic is just so utilitarian, incremental in effect and dull now. Even 9th level spells tend to be a bit disappointing. I'd like a reversion towards a more TSR-style spellcasting where a spell may be harder to get off and in rare supply, but it makes a decisive and paradigm-changing difference to the situation rather than the incremental impact it has now. Clean up the spellbook of spells that lets wizards do what other classes do but better and focus on wizards being the one who breaks the rules instead and creates outcomes that aren't otherwise doable. Combat example - Magic missile is dull because any archer can do ranged damage. Sleep is cool because it produces an effect others can't.
Speaking as someone who's going back and forth on whether to include magic missile, fireball, etc. in an all-wizard homebrew: I'd keep the workhorse evocations, they're way too emblematic of D&D. Same way I'm not proposing to ditch alignment, eliminate spells that let you raise the dead, transition to a skill-based system, introduce narrative mechanics like fate points, or w/e.
Keep: Bounded Math
Kill: Rulings not Rules, it's toxic laziness. Lack of choice in character progression. Alignment not being mechanically important. Alignment is one of the concepts from D&D that has the most penetration into the popular perception of D&D and its not important to the game apart from starting arguments about bad behaviour in the game. The four big questions that should inform your character at level 1 are, What are my stats, what is my race, what is my class and what is my alignment. Alignment should unlock a range of advancement options, such as a Chaotic Evil Wizard should do more damage with AoEs and bonus damage if they catch a friendly target in one. Lawful Good clerics should be better at applying buffs etc etc.
No I mean a normal Fireball would do 8d6 damage, a Chaotic Evil Wizards Fireball would do 10d6 and if they catch a friendly target in the AoE the fireball instead does 12d6. Their tie to the forces of Chaos and Evil empower their magic when they disregard their allies to better damage their foes. Alignment shouldn't be just your personality or outlook, its also your tie to the primal energies that empower the Planes that underpin D&D.