Your character doesn't need to look like you, be referred with the same pronouns or have the same gender for you to feel what the character is supposed to feel.

Then what's the point of games with character creators? It turns out there's a market for this after all. Some games have their narratives written around a pre-built character, and some games don't. There's room for both.

I think OP has a valid question for MW5, whose protagonist's presence is so weak it wouldn't have taken any extra effort (much like HBS BT) to do so.

There's a nuanced conversation to be had here. But as usual this community just wants to be dicks to each other first and foremost. How predictably disappointing.