I'm a very flexible player. I don't mind letting my opponent make a moyo. On the other hand, I'm the guy who likes his influence, doesn't go out of his way to kill groups and doesn't worry about territory. I still manage to win up to dan level somehow. It's hard to explain, really...
The thing you have to remember is that for millenia, White has had second move. For millenia moyos have been built and torn down. Thousands of moyos have either blossomed or fallen apart daily for longer than history books go.
It's not about comfort. It's about finding the best moves and winning (or at least die trying).
Edit: I thought about it, and I think I turn influence into thickness when my opponent inevitably forces me to, then use that indirectly to catch up on territory. It's like chasing and trying to kill groups except safer, and I get to milk my position comfortably until the very end.