> Why did Amiga, the series of computers beloved by artists and musicians, have overlapping windows and colorful icons?

To be fair, these things were computationally intensive at the time. The Amiga had a hardware blitter and very good color capabilities, so it could afford to show them off.

The creators of Amiga introduced them, and added hardware support to make it performant. The only thing which felt sluggish in an Amiga was the floppy disk.

Likely these creators understood the importance of overlapping, draggable, resizeable windows for the audience, and the audience indeed enjoyed them. Same thing with the classic Mac.

If you tried a tiling WM, you realize that it requires learning, tweaking, and discipline. Those are expensive qualities to require from users; one should ask for limited amounts of them.

Overlapping windows also require learning and discipline, perhaps more so than tiled screen splits. We are just more used to the former than the latter.

Amiga may have had some overlapping windows within a screen but it also had multiple screens with significantly restricted arrangement options, if memory serves me right.