> Black moves first, on a 3x3 and 5x5 both end up 100% black with any white piec...

> Black moves first, on a 3x3 and 5x5 both end up 100% black with any white piece being captured.

That is true. The same, however, doesn't hold for larger boards (such as 19x19).

> But, perfect play on both sides probably means any white stone gets captured so white plays zero stones.

For boards larger than the small boards you mentioned above, this is completely untrue.