I agree with flyingcamel, some of guys coming from TP to jet don't switch from TP "mentality" to a jet one.
While I guess descending in a TP at flight idle at fixed speed wouldn't be a pleasent experience for pax, this is normal ops in a jet. And since handflying in a busy environment is not really a good idea (unless you don't have a choice), one should be inimately familiar with automation - how to achieve desired outcome with timely and correct actions. I've seen unstabilized approaches from people forgetting to reduce MCP speed while extending the flaps, or speedbrakes + V/S 1000 + 70% N1, etc.
Regarding the speed debate... OK, TPs can be very fast during the approach as well, but - let's say you have a 2500m runway. Which aircraft will have higher total energy over the fence - a 20t turboprop at 120 kts or a 60t jet at 145 kts? And which of those will have lower margins to stop? Now do the same excercise, this time with a wet runway and one reverse inop.
Everything being said, I think it all depends on the specific person. Some guys can fly anything from the start, some need more training and still make it eventually and some can't fly at all - being a TP or a jet.