Well, to make this all make sense in a game, you need to come up with WHY the player would need / want to change the environment.
The system you are talking about is far to performance intensive and, actually, headline-grabbing (done before, I know, still pretty rare in games) to actually waste it on a sideline role like the unimaginitive "player shoots building, building shows battle damage", without that damage having some gameplay role.
Lets grab some examples of how similar systems have been used before with gameplay effects:
- Spintires: while you drive through the mud, it actually deforms (more or less) physically, and your tires will react to that mud physically.... if you dig a "hole" in the mud with your tire, your vehicle will get stuck.
- BF4: you manage to do enough damage... a building collapses, changing the whole level geometry and thus how the level plays... haven't seen that one in action, but sounded very exciting, if quite taxing on the hardware.
- Worms: quite old and 2D, but still had quite cool landscape deformation capabilities. Sometimes you could only reach an enemy by blasting away parts of the level, sometimes you had to be very careful NOT blasting away part of the level to not endanger your own worms.
for these examples, lets see the players motivation:
- Spintires: the player actually don't want to change the level, but it is unavoidable for him. if he has to drive trhough mud, every action he does in the mud will change it, potentially getting the vehicle closer to being completly stuck. The players motivation thus is to drive through the mude with as little changes to its geometry as possible.
- BF4: As far as I understood it, the only motivation in blasting up the level until the geometry changes is to change how the level is played. That might lead to a more benefical gameplay for some builds, or might just freshen up the expierience.
- Worms: Blasting away parts of the level played an important tactical role. having many meters of solid ground between you and your opponent was the best way to protect your worm from being blown up, and slowly chipping away the solid ground around a concentration of opposing worms might have opened up the possibility of a very powerful chain reaction in later turns.
You could of course also just use it to make things look cool. Have the hero dispose of rocks by punching them to pieces with his fists.... it will not really show off your system as much as it could though, the same could be achieved with traditional means....
I think if you really want to show it off, you need to
a) make it centerpiece of the expierience, thus make sure it has a deep impact on gameplay
b) make sure you ahcieve an effect with it that is hard to achieve with a Voxel system or traditional means (like precut geometry replacing a blown up mesh)
c) make sure the player has a motivation to use the mesh changing capabilities, or prevent it from happening.
Of course, some kind of avatar or object creation system might be a possibility...