Why should a miner choose the longest blockchain if another chain has a higher expected reward? Why did miners/pools choose the longest chain for continuing it?
Because with this strategy they have the highest expected bitcoin reward.
The expected bitcoin reward is (new generated bitcoin (b) + transaction fees (t)) * probability (p) the block will not become orphaned.

Since today b + t is clearly dominated by b and b is kind of constant, today miners maximize p by mining for the longest blockchain. But what about the days when b gets close to 0? Then, right after a completed block, b and t are 0. Thus, a clever miner should ignore the latest block, since even with a small p he will end up with a higher expected reward.

But once miners become aware of transaction fees and will not build on the longest chain this could cause serious trouble? Did I forget something or are these assumptions right?
I think it's conceivable that this could happen. But under realistic cases, I don't think it actually will. If you don't mine on the longest block, the probability that your block will ever be part of the longest block drops drastically. Unless a block you mine becomes part of the longest chain and stays that way, you never get any fees or reward at all.