Is it legal to begin pilot training on a jet? Disregarding financial and difficulty concerns, would it be possible (legal) for someone to obtain a PPL license on a jet aircraft?

If it is possible, would there be any restrictions on the license on operating piston engine aircrafts?



EDIT: the linked question asks about EASA regulations. This question is about FAA regulations, thus, the answer in the linked question does not apply.
There is nothing in the US regulations and no references that I can find that prohibits a pilot from learning to fly in a jet aircraft.  There are multiple systems on a jet aircraft that are not found in small GA aircraft and the same systems are more complex.  A lot of professional pilots who fly the same jet for a career don't fully understand the different systems on their jet.

The issue isn't with the FAA though; it is with the instructor and insurance companies.

I certainly would not agree, as a CFII, to train a new student pilot in a jet.  I personally don't want to take on the liability for the payment I would receive for my services.

Most insurance companies will not ensure a student pilot to learn to fly in a jet.