I have had people moving front to back many times, while I was flying. There is nothing inherently wrong with it and if it can be done easily it is far safer than landing and taking off again.
My girlfriend often moves to the back on long trips, where there is more room and she can read or sleep. Or prepare lunch
The real problem is that most light planes are a bit too cramped to make it easy. Even the TBM850 (which I have flown LHS) is difficult in this respect; one's legs only just squeeze between the centre console and the seat.
Also the person moving has to be quite "compact" and flexible. Many people are way too obese to be able to move at all. If they tried, they would smash up the headset connections etc. One of the reasons why the internals of the "single door" planes like the PA28 family are often in such poor condition is because heavy people have to climb in awkwardly, putting their weight on the seat backs, standing on the seats, etc.