The advantages are that it can have extremely dense chip to chip connections, as much as ~10,000X as dense as TSVs (literally) and no ESD diode capacitance (can be as much as ~50fF!!).
The disadvantages are that copper interconnects melt above ~400 degrees celsius, and we are around ~1200 degrees celsius to make transistors. There are a few ways around this but they usually result in crummier transistors.
*due to violation of Fourier theory of heat.
EDIT: I did look at this idea some time back and I believe AMD even has a patent on it (though I might be mistaken), it's possible, but might cause unexpected issues.
I'm a physics major, but haven't gotten to do much semiconductor coursework yet.
When you fabricate several 2D chips and then integrate them, it allows you to test those 2D chips for errors separately before the integration, which should give you better yields overall.