Learn to play Civ V, instead of trying to play it like Civ IV and then complaining when it doesn't work.
There are things that are wrong with V, but being limited to three cities is not one of them. Yes it's harder to grow, but I don't see that as a bad thing. Here's a shot of part of my Empire in my last game. As you can see, growing beyond 3 is not only possible, you can get good gold and happiness (and science) while you do it.
Seriously, you've conquered your entire continent (in a map that looks like it's on large setting) and you only have 9 cities to show for it? And some of them are tiny (1 size-17 and everything else low teens)? And you think that's a good design decision to limit players that way?
I've had that in my previous game in a large map, too. I kept a settler that I didn't use for 300+ turns because I couldn't justify planting that next city. I razed everything on the other continent because the game put too many penalties for annexing them.