heck, even 25 years ago there were thermorests that were not as thick, and could be folded in half before rolling up.Mmine was a full length lightweight one, still the self inflating ones, and my wife had a 3/4 length one, even more compact. I always put in in a pannier along with my sleeping bag., kept only tent on rack.
They were pretty slim, so not great at all for sleeping on your side, this is what I like so much about the neoair type ones, I can sleep on my side fairly comfortably, and depending on how much air you put it, you can set the firmness of it, for me it works great.