If your use-case is "crop screenshots", your competition isn't Photoshop, it's MS Paint.

There aren't many image editors that are able to crop pictures in a usable way. MS Paint for example can't do that. I wonder if the "move this rectangle" method is under patents.

Maybe you mean something different by "cropping", but drawing a rectangle followed by ctrl+c then ctrl+n is fairly quick / good enough

If there was a linux port of paint, I'd consider it. Until then, GIMP is fine.

Check out Pinta. It does basic image editing pretty well, imo.

jspaint.app has you covered