I am more specifically referring to laptops. Everytime I have seen an LCD come on on a laptop then shortly off yet the image on the actual LCD is on, it's almost always the inverter. I have yet to see heat come from a LCD on a laptop so intense that it causes the wires on the CCFL to melt.

Laptop LCDs are also more complex/compact than desktop LCDs in that it's lower power, and the parts are smaller. The desktop LCDs also have huge boards that do power conversion/data conversion from VGA/DVI to whatever connector the LCD uses. Those boards can sometimes be as big as a laptop itself.