The 737 (jet) is just a different beast, not easier or more difficult to fly than a TP, just different. For a start, the aircraft systems have to be learnt and understood and then the SOPs have to be learnt and used.
Yes people have transferred from LHS TP to LHS jet but almost all the major operators these days will do it only on an exceptional basis. Jet2 brought in a lot of LHS guys with jet experience when they introduced the 737 and these days they virtually never bring in LHS TP guys to LHS jet.
There is a reason for this, namely to sit in the LHS of an aeroplane you must have suitable experience of how it flys and how it works. When you are paired with an inexperienced FO there is a huge burden on the LHS and he/she needs the capacity/experience to manage the flight safely.
Surely it boils down to risk assessment? The risk to the operator is substantially reduced if LHS TP guys spend some time in the RHS to learn the new aeroplane and then when he/she is ready (judged by assessment on the line and in the sim) then make the transition to LHS jet.