Hit points already represent "ability to avoid a blow", that's why fighters get more than magic users.
Some versions of the rules have said so to varying extents, but I don't take this as being a given. The definition of hit points is one of the fundamental problems with D&D rules.
If it's a mechanic that lets them "put in an extra effort", why would they not use it? And if they are using it all the time, how is it different from just giving them extra hit points?
They would always use it and it would be an assumed part of combat. Here's the thing: it's a resource. Just using the TB combat rxns as an example, you only get one per round at the start, and it goes up to four at a rate similar to iterative attacks IIRC. A reaction can be a dodge, block, attack of opportunity, or possibly another action. You will probably suffer more attacks in a round than you have reactions to use, and you have to choose how to spend those reactions.
Thus, a simple but significant strategic element is added. If you take an attack of opportunity, you lose a chance to dodge an attack yourself. If you dodge and get hit, you'll wish you'd blocked. If you dodge an enemy's extra powerful smite, you'll feel pretty good about yourself. This concept is decidedly not the same thing as adding more hit points, but if your goal is to make fighters and their ilk more powerful, more tactical, and more fun, this is one potential way of doing it.
If hit points represent actual damage, and this is the ability to avoid damage, then you seem to have a vitality/wound point system with the points renamed.
D&D already has a vitality/wound system; it's just poorly implemented (subdual damage or nonlethal damage; which are hidden and don't get used much). A well-implemented one has been a common topic of discussion in this forum.