ok, we're not talking about compatability with API's really.. it's mostly compatability with hardware that nVidia's drivers seem to have the most problems (ok, DX compatability isn't as good as 3dfx's AFAIK though).
now, when you push technology so hard, you have to cut something here and there. when you are low on time, you might not have time to test everything. so, you'll find problems in certain games that wouldn't normally occur, or you'll have problems getting your AGP card to run with all the bells and whistles.
I'm guessing this was part of the reason why 3dfx stuck with the Voodoo architecture. They somehow knew that AGP really wasn't needed much, and though it DOES help performance in games now a days, much of the performance comes from the increased throughput, and fast writes (which bypasses the RAM when sending data from the CPU to the video card).
the Main reason AGP came about (besides intel wanting to enter the video card market, but that's a totally different story) was becuase they thought that video cards would not be able to have enough RAM for textures.
Time has passed, and we now see video cards, with 64 megs SDRAM. as you can see, the main use of AGP has not been used at all. only the two things I mentioned above are what really gives AGP a performance increase, and even then, when T&L becomes popular, AGP will no longer matter much at all (perhaps why AMD has made some rumblings about a totally new architecture?).
T&L, offloads the CPU as you know, and so the CPU therefor doesn't have to send that massive amount of geometry data to the CPU.
Intel hasn't actually given other chipset manufacturers the ability to have normal AGP support. it's like when AMD was trying to build CPU's that ran on intel compatable motheboards (talking Socket 7 here). these ones worked FINE, becuase AMD already had good compatability with these chipsets, HOWEVER intel didn't like that, and quickly abandoned the Socket format, which forced AMD to keep the Socket 7 platform alive by itself.
Intel has made sure that AGP will not come easily for Via, ALi, or AMD chipsets. what AMD and the rest would need to do to get rid of these compatability problems, is bypass the AGP. get rid of it, and replace it with their own graphics card port. it's going to happen sooner then you think, because as T&L becomes more and more useful, the less an advantage (what little it had) the AGP port will have over the much slower PCI bus will have.
so, in order to really guage whether it is nVidia's fault, or Via's (or AMD, or ALi's) fault for compatability problems, why not actually try running AGP 4X (with Fastwrites etc) on an Intel board? can you run AGP 2X with Fast writes and sidebanding etc on the BX board? (I don't think so, but I don't know).
ok, so the AGP problems have been partly explained. what other compatability problems are there? well there is that whole issue of power, but that can be blaimed on mobo manufacturers too.
then come the drivers. Drivers incompatabilities? really? I didn't think they were that bad? what kinds of problems do you mean?