I've got a player who regards limited-use martial abilities as doing a violence to their verisimilitude (even on the encounter level), so I'd personally be interested in adopting some of these maneuvers as "baked-in," so that the only limited resource the fighter is spending is the action economy. Though I don't imagine that'd be for everyone. And I don't even imagine it'd be that hard to bake-in, as by the sounds of it, the fighter perhaps spends the dice on damage, not on the manuever per se.
My suggestion: At the start of each of his/her turns, the PC loses all superiority dice, then rolls 1d8*. If the result is less than or equal to the number of superiority dice the character would normally have, s/he gets one superiority die which lasts until the start of the next turn. If not used by then, the die is lost.
The idea is that every so often, you spot an opening to try a maneuver. The better you are at maneuvers, the more openings you see. But you have to seize the chance when it comes--you can't save it for later. This avoids the verisimilitude-damaging "gas tank" model of limited abilities, while also keeping the PC from spamming the same maneuver endlessly.
[SIZE=-2]*The die size might need to be adjusted for balance. I figured one short rest every two combats, and five rounds per combat, which would suggest 1d10; then I considered that there is a substantial cost to not being able to choose when to use your superiority dice, and reduced it to 1d8. But it's basically just a seat-of-the-pants guess.[/SIZE]