True but again that was the day after Eto'o had joined, four strikers going into one position doesn't make for great playing time. I like how you said it was a sign of him not being mentally strong, him demanding to go out on loan so he could get game time links to quite the opposite. He knows what he wants and went for it.
You could speculate that he'd be the main striker and would get the most playing time but it's highly unlikely.
Torres is likely to start half your games, so that leaves 20 or so for the other three, Eto'o could quite easily demand a place in half of those leaving Lukaku with scraps. Why stay for the chance to play 10-15 games when he can go out on loan and get 2-3 times that.