I've thought about this every so often and I always come to the conclusion that if I wanted to do this I probably wouldn't use Windows.
I don't know much about linux, but I think it should be possible to create a very minimal installation of the operating system and mame + rom.
This would have a few benefits.
1) Very Fast loading time. I think it should be possible to go from a cold boot to the attract mode of your game in less than 30 seconds.
2) Stability. The less drivers and background services running the better. This will result in the game running faster and less chance of the system crashing randomly during gameplay. This almost never happens anyway, but if you wanted to leave the system on for a long time the chances increase.
3) Video Sync. I may be talking out of ---my bottom--- here, but I've always heard that having an operating system running in the background contributes to screen tearing and jittering. With one ROM you should be able to set a specific resolution and not have much need for V-sync or triple buffering. Of course I would still leave it on.
4)Input delay. This is related to video sync. The less stuff running in the background the less chance that something will slowdown the emulator and create input delay.
5)Volatility. It's possible that a person could even flash the entire operating system + emulator and ROM onto an EEPROM and run it as an embedded system. If you did this right it might be possible to do a VERY fast boot, like less than 5 seconds. This would also eliminate the need for a hard drive, which would cut down on noise and add the ability to just switch the machine off whenever you feel like it.
I've found that Gentoo Linux (as opposed to Ubutnu/Fedora/etc) is VERY good for what you described. I had it running on my MAME cab for a bit (switched over to Windows because half my house couldn't figure out how to use it) and it was incredible. So looking at your list:
1. Fast Loading Times- Check- my cab uses a P4 (2.0 GHz) and it would boot in under 20 seconds. Granted, I didn't boot to a MAME frontend, but I'm sure that would only add a few seconds.
2. Stability- Check- provided that you installed it correctly there's no shot that it's going down.
3. Video Sync- no idea
4. Input Delay- Never ran into any delays, so I doubt you would hit any. You build the OS to your needs, so there's none/little excess processes running in the background.
5. That would be pretty hardcore. You could make a Live CD using LFS (probably would take you a few months) that would accomplish this as opposed to using an EEPROM. I know some Asus motherboards have some sort of 5 second boot for certain apps, like Firefox, but I've never used one.
I think Gentoo would be the ideal solution because you literally build it from the ground up. It takes a while to set up, but once you have it running you pretty much have the ultimate OS- you tailor it to your needs in ways that I feel can't be matched by other distros.
Sorry for the Gentoo/Linux promotion but I thought that would be of interest.