I have no experience with realtime video editing, but as for just displaying something on a TV/projector/whatever, a PC can really do whatever you need. Just for the record, I have a GeForce FX-5200, three years old and not even a high-end card to begin with. It can drive up to two displays at once using VGA, DVI, or S-Video connectors. That is, two displays with different resolutions and refresh rates. I have an old 19" monitor hooked up to the S-Video and I have no problem getting games, emulators, AVIs, DVDs, or just the windoze desktop to display properly on it. I can even customize the overscan and pixel clock.
Also, I don't think it's accurate to say that TVs are becoming VGA monitors. That would have been nice, but it would have been WAY TOO EASY. Instead of taking the obvious road to a higher resolution TV standard, we have more signals, connectors, resolutions, and acronyms than we could possibly need, not to mention DRM schemes and various other incompatibilities.