There seem to be two sides to the cover issue.
The XCOM aspect is more board-gamey, where they rough out a level in plain blocks, getting the distances between the blocks, chokepoints, etc., right for good gameplay first, and then dressing it up in some sort of quasi-realistic setting. In that case, the gameplay layout comes first, and sometimes the blocks of cover can indeed look weird, gratuitous, etc., from a realistic point of view, because they're reaching to find a realistic. cohesive "paint-job" for the placing of the blocks. Plus in strict XCOM board-gameyness, it's all squares, and in real life everything isn't set out rectilinearly, so that can look weird too.
Then on the other extreme, you have more of a simulation, where you have a realistic setting, and the gameplay has to fit willy-nilly into the realistic setting using more realistic rules and gameplay - in that case, cover when it exists doesn't look out of place, and can be at all sorts of realistic angles.
I must admit, once you've played a game with a cover mechanic for a while, not having a cover mechanic seems weird if there's stuff lying around that could potentially give cover/half-cover from a realistic point of view.
As with many things, Troubleshooter has a nice way of doing it: cover can be at diagonals, while having the grid be a grid and the cover marker marking full or half cover over the grid, not the object.