Advantages: It looks ridiculously cool.
Disadvantages: No top. No hope of a top. You won't drive if it might rain. You won't drive if you have to park. You probably won't use the car for very much of anything besides looking ridiculously cool.
There's a reason almost nobody has one. A full (fabric) tonneau could be fabricated to get some coverage for parking, but nothing at all for driving, unless you build your own bimini top (with an open back). If you have one, your usability will drop even lower than car without one (and that's already pretty low). You may as well get the plexiglas racing windshield, if you do it.
I have one in my stash for a future build-- but the car will have to be a very, very specific kind of machine, meant for fair-weather back-roads blasting and (covered) trailered trips to the mountains.