I would like to interject a bah-humbug here; riposte, parry, evasive footwork.
Riposte and Parry are reaction maneuvers (by 20th you end up with 9 of 16 maneuvers, having 3 of them be basically unusable intuitively seems wrong to me) and evasive footwork doesn't rely on opponent openings. With either system (the refresh d6 and the opposed roll) he wouldn't really have the option to use 2 of them ever, and the third one applies against all opponents so having it based on enemy opening seems counterintuitive.
I really feel like the die based system is not only the most balanced, but the most functional. Otherwise, those are 3 really good maneuvers that you just never get to use (at least 2 you can't since they're reactions, the other just doesn't make sense given the system). You could fix this by letting them do those maneuvers whenever, but then there's no good reason to ever not use them, and since you'd necessarily be decoupling maneuvers from superiority dice, there wouldn't be a limit.
If you want it to be a little more realistic, you could add a mechanic to allow for the refreshing of superiority dice similar to the d6 refresh model, or by making a different system (like a second-wind type SD refresh, recover 1d4+int/wis (I think wis makes more sense since it's about noticing openings) SD as a bonus action 1/rest). OR, you could allow him to always have superiority dice, but those always on SD are d4. He'd be able to, effectively, grant himself inspiration for attack/damage. A d4 isn't really going to break anything, but it will let him feel like he's always got the opportunity to use his maneuvers, or he can perform the maneuver, but gets no superiority dice for the maneuver, and some maneuvers become worthless without SD, others are not, but he is ALWAYS a battlemaster this way in that he always has a tactical attack option, but then he can riposte all the time limited only by having a reaction. The last option I would say that he can choose to spend a superiority die when performing a maneuver to gain the benefits that the SD grants for that attack (you can always trip an enemy, but you can only add damage when you spend the die), which would let him more strategically choose to boost his damage/to hit and still be an always on battlemaster (because really, without SD, the battlemaster is just a champion fighter without remarkable athlete or expanded crit range).
The issue is that the SD system is already "balanced" so changing it up requires a lot of math to see how it would actually affect the game in practical terms.