fermentation creates a good deal of heat. i don't see any benefit to using a cooler, but i do see a huge downside. there is no way to cool it down once it gets warm in there. beer frequently ferments 5 or so degrees warmer than ambient temperature, and thats in a fermenter with really thin walls. once your beer starts fermenting it is going to get warmer, not have anywhere at all to spread that heat, and then the yeast will ferment even faster (generating even more heat compared to if it was in a bucket), and the heat will all be trapped.
also you can't see whats going on, you won't be able to have an airlock (you will have to make sure enough air can get out, but none can get in), the potential threat of it leaking through the ball valve, and uncertainty as to the sanitization. milled grains harbor a lot of bacteria, so if you are using it as a mash tun and then fermenter you need to be very very careful.
sounds like a ton of problems just to have the better handles.