How come there isn't any plasma monitors

Plasma can't achieve the same pixel density as LCD screens.

For that reason you don't see any 1080P plasma screens under 42"
While LCDs can achieve 1080P as low as 4.5" more dense than the iPhone 4.

It is true that plasmas have a bajillion times the static contrast, better color that most LCDs, and doesn't have to deal with response time.

It is also true they suffer from screen burn. Basically ensuring your Windows Start menu would be permanently burned in even if you don't look at still text documents for long hours.

The gasses also fluctuate in brightness randomly. Not noticable in motion pictures several feet away but noticable up close looking at still images.

There are 120hz LCD monitors. They are quite good in terms of refresh rate.