The biggest problem I have with holodeck characters or the EMH and other examples (such as VOY: Flesh and Blood) becoming self-aware, is why doesn't the ship's computer seem to be self-aware?
I don't see the problem. Self-awareness is something you demonstrate. If you see no point in demonstrating it, you won't be recognizable as self-aware, but that doesn't mean you aren't.
Or, more in line with the arguments from the previous page, when you demonstrate self-awareness, you manifest the potential, and the manifestation is the self-awareness by our current definition. When you don't demonstrate, you aren't self-aware by our standards, but you still have the potential, yours to command whenever needed.
Why would a complex and capable computer stoop all the way down to demonstrating self-awareness, i.e. the ability to chit-chat with humans? It's not an impressive feat or a useful trait, except perhaps when your job is to interact with humans...
...And there the computer of the E-D certainly excels. It answers questions the heroes don't have the sense to ask, it tells Data to stop babbling, it even opens doors at the dramatically correct moment. It just does all that with the panache of a seasoned butler, without making a fuss of itself.
Holodecks are different, because their very point is to make a fuss. So the computer makes one.