Power is the solution to all problems. Aside from that a turbine engine with variable pitch fans is something too unfeasible (if not close to impossible) to build (or make it work right), most do have variable stator vanes, which control air flow to the high pressure compressor. There's no need for a jet to have counter rotating blades and most turboprops do not (I can't think of any that do actually), I'd venture to guess it's due to the increased cost of developing and certifying the same engine twice.

Now talking about "correcting how a piston pilot does", for the most part we do, all twin turbine have a VMC, but we also have a higher speed envelope that we can achieve on one engine, which mitigates most of the problems.