Some threats are so major that you cannot respond to them with Fighting, you must Dodge
When surprised you have to Dodge as a response.
Dodging always reduces the damage you take by 1, even if you fail the roll
You must spend an extra success to move if you use Fighting, or to deal damage if you use Dodging
Rules 1 and 2 are just a way of expressing what you said. Sometimes you just have to avoid things, and it is better to use Dodging than Fighting to do so. Rule 3 makes it mechanically better to use the right skill. Rule 4 encourages you to pick the "appropriate" skill, not just the one with the most dice.
I think Rule 4 is the most important. The rules already said "You can choose any Stat + Skill to make a roll, provided that it makes sense for your Intent", that's the flexible part. The "extra success" cost then underlines that doing additional things off-skill is harder. If you want to run away you use Running, and if you want to do non-running away things with your successes it is harder than doing running-away things.