They don't always, but the obvious/boring thing to do is to start with a shape that tiles the plane, like rectangles or hexagons. A Penrose tiling might be an interesting approach to take.

I discovered these a few years back: https://n-e-r-v-o-u-s.com/shop/ and I really dig 'em. They might be using a grid in some cases--but if so it's pretty hard to tell.

I'm working on my fourth. It's hard to worry about the apocalypse when the complexity of the puzzle requires your whole brain to make progress.

I would assume that grids are producing pieces that are most similar to another, making the puzzle more difficult, while also being easy to design.

Of course, this doesn't answer "Why 90 degrees?"

I’d guess because you could easily build a machine to cut the pieces with long strips of metal rather than welding together a bunch of disjointed pieces.