Yes, that is what I meant, OpenGL instead of DirectX on ALL platforms. This would make it easier to port software to all major platforms. However, as Gilrond said, XBox doesn't support OpenGL, and it played a part in helping MS consolidate their alternative in the gaming market. In fact, as far as I know, the XBox is one of the very few devices that doesn't support OpenGL. Even a Nintendo DS does.
I have been playing since before DOS/4GW. I fondly remember Glide on my Voodoo 2, which I thought was amazing! Eventually games moved on to OpenGL and then, suddenly, switched to DirectX. I know the practical gamer doesn't see a difference and modern video cards support the latest OpenGL and DirectX, but as a GNU/Linux user and enthusiast and long time PC user I like games to include viable Personal Computer platforms that my friends and I would use.
Back then, "Linux" wasn't really a home OS but there were versions of games like Prince of Persia 2 for IBM-PC and Macintosh. Nowadays, GNU/Linux is a widely used platform that draws the attention of the general public and power users, including PC gamers. I believe it is time for companies to include Linux in their plans, and in order to do so they might as well start by switching to platform-independent, open-specifications like OpenGL that make it possible to run software natively on almost all modern platforms. A community of very dedicated users have made it possible to run certain Windows binaries on GNU/Linux, through Wine and other tools, but we should not have to go this far to play games, especially when there ARE cross-platform technologies.
So yes, I didn't mean quality assurance standards, but that goes without saying.