This is how we play it for my wife's Fighter. Your question is a bit like asking "can I still cast spells without slots?"No, you can't use a maneuver without expending a superiority die. Every maneuver has the phrase "expend one superiority die" in the description as a condition of doing the actual maneuver. I'm not sure how it can get more clear than that.
I think it's meant to be every combat, not every round. By the standard rules you roll initiative (And thus get back the superioity dice, if you have none left)just once at the beginning of the encounter, not every round. But I don't see granting this bonus every round will inherently brake anything, except for maybe letting the battle master slightly outshine the champion, damagewise.It's what makes the level 15(?) ability to get one die back when you're out so cool. It's effectively 1d12 or whatever your die size is at that point extra damage a round as most of the maneuvers require a hit to use the die.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.