...you know the temporary pool lasts until the start of your next long rest, right? unless your campaign is the one-battle-per-long-rest type (which i've played in) then it's not going to be just one battle.
i'm going to assume that by "smites" you mean empowered smites and just mention that, again, you can turn spell slots into exertion at the start of your turn, so you can decide when your turn comes around if you need the exertion or if you want to save the slot for a spell or empowered smite. there isn't really any good reason to dump all your spell slots at the start of combat for exertion, i was just using that as an example - but what you CAN do with it is expend spell slots so you have as close to exactly enough exertion as you'll need to do what you want that turn, even with only being able to convert one spell slot per turn (which is, again, why perfect assault is insane on a herald - and your house rule wouldn't help all that much, since you could still easily get all 6 perfect assaults off, it'd just be tacking on more maneuvers that'd be a pain).
given all that, the extra exertion from a fighter dip is really just icing on the cake in my opinion.