Yeah, HDMI doesn't cause lag and gives the best picture. No reason not to use it. That goes for Xbox360 and PS3 games, but the Wii and older systems don't support HDMI so it's a different story there obviously.
VH236H is only mentioned so much because it hits on a lot of good notes -- cheap, very low lag, and good quality picture. But I believe the VH236H is actually being phased out in favor of the VH238H which is only slightly different (LED backlight). Both are equally as good in terms of lag though.
But no, this is NOT the only good monitor for fighting games. It's just that most people don't know how to actually test a monitor's input lag, and they don't want to buy a monitor for fighting games without knowing 100% sure that it has low lag. So they just go with what everyone else is going with.
The reality is that most computer monitors should work well, while in general anything marketed as a TV probably will have some lag. Sometimes if you google for a particular monitor plus the words "lag test" or "input lag" you might find information about it, but maybe not.
Anyway, if you are in the market to purchase monitors, then I would recommend either the VH236H or VH238H. It's not only because of the low lag but also just because they are usually very cheap compared to other similarly sized monitors.