Firstle you can't learn in a piston machine and hop straight into a turbine without doing a conversion course from piston to turbine and having the rating recorded. Secondly, you have to have a type-rating for each machine you operate. In theory you can't learn in an R22, pass your PPL and then hop into a Gazelle/Squirrel/Bell and fly it off the next day. Each machine has a different conversion route depending on the complexity of the helicopter and it's systems.
What you can't legislate for however, is someone doing something stupid, especially when they lack experience on that type. No licence restrictions are ever likely to alter that fact, which doesn't produce a convincing argument for a restricted licence. As most turbine machines are hired via firms like Cabair or London Heli et al, it is unlikely they would let you take a hire without first passing a competence test with a TRE first, regardless of experience. They will also want to verify your route and intentions so as not to put either you or their asset at undue risk.
For the record, the Gazelle does have some small quirks, but it otherwise a fantastic machine to fly, I learned on one!