Simply put: they don't look nearly as good as CRTs for MAME.

Outside of the MAME universe, they are expensive, have bad colour accuracy, show signs of ghosting even at low response times, and more often than not have annoying dead pixels. When OLED monitors are available for the same price, they'll be worth the money. OLED will have much better colour definition and response times almost as good as CRT (thanks to using LEDs instead of liquid crystal).
Currently the only thing LCDs have going for them is they take up less space on your desk, and are lighter. Other than that, a CRT beats them for image quality, refresh rates and price every time.