It's definitely an idea, but (despite my major antipathy for excessive caster power) I'm more than a little concerned that we'd just be creating a perverse incentive toward "rocket tag," coupled with a new version of the "who's playing Brother Bactine?" problem.
That is, if only Fighter-types get such benefits, we are left with a conundrum. Either fights are designed expecting that to a meaningful degree, or they aren't. If the former, then the instant a spellcaster actually gets threatened, they're toast; so spellcasters must prioritize personal defense (something they already do!) and then budget in as much Phenomenal Cosmic Power as they can afford. Conversely, if combats are designed without any such expectation, playing a Fighter-type would be awesome for a little while, and then become swiftly boring as nothing can actually hurt or even really inconvenience you.
This is one of the reasons why extensive, intensive playtesting is so important. I'm still chewing on the outline for a thread-essay on the subject of perverse incentives, because they're a really really big deal and it feels like nobody talks about them.