In 2-up games, Carcassonne closely resembles a kind of grappling or wrestling, where you try to tie up your opponent's meeples, usually by making cities incompletable with the set of tiles in the box. Once you have a numerical advantage in meeples, you have an edge on the probability distribution of tiles that come out of the box - you can make more speculative bets. Whereas in 3 or more player games, it's much more rewarding to be more cooperative if you can be, because specific attacking actions are to the benefit of the player(s) that aren't involved.

Then there's the management of liquidity of meeples through the lifecycle of the game. You want to invest a lot, early; but you need to try and get them back towards the endgame, so you can steal fields and place in micro-fields.

There's a surprising amount of subtlety that emerges from the gameplay. In particular, learning how different growth patterns make your resources easier or harder to steal, or worse, block from completion.

The relative straightforwardness is exactly the appeal to me. There are nights when nothing works better. I had people over to play games last week, for example, and turns out it had been a long day for all of us and we didn't really feel like anything too involved. Carcassonne was perfect. Same with playing with extended family at Christmas. You can explain the main rules in a few sentences and everyone enjoys it.

All that said, I almost always use an expansion or two (or three) to keep things varied and add depth.

I tired of it when I realised the obvious way to get better was to learn all the tiles, so I'd know exactly when what patterns I left were blocking or not.

Learning all the tiles, and tile counting, both just seemed too dull and annoying to actually do.

It is a fun game if nobody learns the tiles :)

Randomly remove some tiles each game, without revealing which were removed?

I have a collection of 20 or so games, all well rated and popular on BGG, but for us Carcassonne is the most popular and enjoyable to play. It's beautiful, not too heavy, keeps everyone involved until the end. We just love it. We use three expansions: river, traders and architects, and inns. What a beautiful game!