I was about to accept what you said as the harsh truth.
BUT, I remembered an old variation of MAME called PSXMAME, which is able to render the video using GPU plugins for PSX emulators and ZINC. I tried it with Tekken Tag and, even though it's not 100% full speed, it's MUCH more acceptable than how MAME normally runs the game on my computers.
So now I'm happy. I can provide a link to PSXMAME if you wanna try it...