Some of those already mentioned:
Sinclair PC-200 (black), also sold as Amstrad PC-20 (white) minus the RF connector IIRC
Amstrad PPC 512 and PPC 640, although those are more like portables than all-in-ones
Schneider Euro PC, also sold as Dual Data in France
Olivetti PC-1 Prodest, not sure if it was sold under a different name
(VTech) Laser Compact XT
Note that while Amstrad's 8-bit CPC range also was sold by Schneider under their own name, apparenty Schneider decided to make their own PC compatibles instead of carrying on with the Amstrad models.
There may have been others, but combined with the Tandy models you're already aware of, that is at least 5-6 individually different all-in-one PCs from the same era, not counting those Compaqs that rather combine computer + monitor in one (like a Macintosh) than combining computer + keyboard in one. Of course if you combine all three you get a portable or a laptop computer but that is a different type of computer.
All tend to be 8088 compatibles, sometimes up to NEC V40. The lack of easily accessible expansion options and the potential customer base likely didn't make it worthwhile to carry on with the form factor in the era of 286 and in particular 386 systems. Although Atari kept the form factor until the Falcon 030 and Commodore released the Amiga 1200 in that form factor, I think the PC world had moved to desktops, towers and laptops instead of all-in-ones.
Edited by carlsson, Sun Aug 27, 2017 9:38 AM.