There's also the potential for cancer, of course, but personally I don't buy that objection. You can take cancerous cells and revert them to stem cells and they'll stop misbehaving (unless their genetic damage is very specifically triggering them to grow without bound, but I think this is rare. Usually it's a gene activation problem.)
And complexity of the regenerated part isn't much of a problem. You can reroute the nerves on a salamander to get a fully functioning arm poking out of its back. Some things can regenerate half their hearts fast enough to survive. I don't know exactly how the information is transmitted and expressed, but it's there.
No, I can't prove my assertions. They are based on half-remembered readings of the book The Body Electric from long ago, written by a guy who did experiments to back this craziness up. He was enough of a nutcase that not many people followed after, though his key findings were replicated. And he lost the thread at some point, going on a crusade against emf fields that didn't seem to be based on real science. So it goes.