The reason for keeping the head on the cylinder is to save the price of a head gasket. Hardly worth it in my opinion. It is a good idea to leave the piston in the cylinder so as not to disturb the rings, but if you had you would have not seen that broken ring. Since the late wristpins use external snap rings, I remove the cylinder complete with the piston and remove the piston on the workbench. When reassembling I find it much easier to get the piston and rings into the cylinder on the bench.
It's not surprising that the bike ran well with a broken ring; you just had a second gap in that one!