Well I've been browsing this forum for a while and this topic pushed me over the edge to register. I love the 440BX, at one time every machine I built for family people had some version of that chipset. I finally retired the last one last month.
My first "real" 3D accelerator was a Hercules Geforce2 MX, for a Tyan S1590 Super Socket-7. That's a VIA MVP3 chipset with a nearly unusable impersonation of early AGP. I doubt it's anything beyond the earliest AGP spec (if that). It was difficult getting it to work, but ultimately it did and power was never a problem.
I do remember back then reading about people having AGP power problems on some boards, and that was in fact one of the reasons I decided to get the MX instead of an older higher power card like a TNT2 or whatever.
The stories claimed some motherboards had cut corners on the AGP power supply, not realizing how demanding video cards would soon become. I don't know if that's true, but maybe the early AGP spec is the real issue like you described. I'll admit, I'm afraid to try popping anything heavy in that old board.
HP Kayak 440GX: I ran the GF2MX and later a Geforce4 TI4200 128MB on this machine. This was a 1998 machine, but it came with a crazy big OpenGL card in it so power was probably ample to begin with.
Asus P2B-F rev1.00: Prob midlife BX or a bit later. I set up 2 of these, 1 with the Geforce2 MX and the other with the TI4200. I ran them overclocked at 133FSB, putting the AGP slot at 89MHz. Both cards and boards handled it perfectly, they were used about 2 years. NVidia cards of this period were good at handling 89MHz.
ABit BX133-RAID: definitely a late BX board, but FWIW, it ran an early Geforce3, again on an 89MHz AGP. No video issues, ran about 3 years.
Asus P2B in general: At one time I went through about 30-35 of these boards and resold them. I didn't use them extensively of course, but I did boot them into Memtest86, and also into a knoppix GUI. I probably used one of the Geforce cards for this but I don't remember for certain. The oldest boards were rev 1.02 which definitely had early parts/design, they were noticeably inferior to the later boards. I never ran into a P2B that had video issues, but 3D stress tests weren't on the agenda.
Asus P3B-F: I had 3-4 of these, same testing as the P2Bs.
Epox EP-BX3: this is probably a later BX board, but I've used it with numerous GF2-4 cards (including GF2 Ultra and TI4600) without issue. However, I didn't run them hard, so I can't claim to have pulled max power with it.
