More choices could allow you to make a mechanically strong character even with bounded accuracy.

Well, no, not really. The whole point of bounded accuracy is that it limits the bonuses you add to dice (all dice, so yes damage is constrained by it) so the rolls matter more, and choices that allow you to gain advantage, change damage types, exploit weaknesses, even reroll low damage are all included already. What you mean is that more powerful choices would allow you to make mechanically stronger characters, which is just a tautology - the reason for the limitations on the choices is bounded accuracy, so new choices that were added would still be limited by it.