Oh well unplayably choppy is more subjective but I was going with the true problems a large dt would create like collision detection failure and controls not working.
I can't think of a framework that doesn't have a fixed timestep except for maybe gamemaker or some of the simpler frameworks. Maybe some of the html5 stuff is non-fixed timestep but that is a field that is just coming into its own right now.
None of the bigger 2d or 3d physics engines today that I know of use a non-fixed timestep.
In platformers with high speed movements fixed timesteps are even more important because of tunneling. You can often account for tunneling in some of the better physics engines but it is sloooow.
In fps games there is a lot of interpolation going on with the server correcting player and object positions. If the server lags you and everything else is going to teleport no matter what. The server is not even accepting your control input at that point so either you are going to desync or you are going to teleport when the server tells you your real position. Generally in fps games only critical physics objects are being server corrected anyway, this is usually a small fraction of the physics objects. For example if an enemy fires a rocket at you that is not usually server corrected. If you get hit in the server calculations then you got hit whether or not you think you dodged it client side.
My point is that if the server hiccups your jump being slightly off is not the big problem, The big problem is that the controls are unresponsive. Also when the server hiccups it is rarely the actual fixed timestep serverside that is your problem, it is the internet. If your computer hiccups then it is not updating positions from the server so all critical objects are going to teleport. Could there maybe be slightly less teleporting on non-player controlled critical physics objects? Maybe so but if you are losing that many timesteps than things are going to jump around on your screen no matter what because your framerate is like 5.
