It is potentially a very good option.
However the cost is prohibitive for most - several £100K at the very best, and turbines are not efficient low level so you probably immediately restrict the market to the touring instrument rated pilot market. That is a very small community and then they need to be high net worth individuals. Unfortunately all of that doesnt add up to the greatest incentive to create a new turbine single.
On the other hand diesel power plants (as developed for Diamond aircraft) achieve the benefits of using Jet and are efficient low level. Its unlikely they will ever provide the speed of a turbine and there are some issues an the high FLs but for the reasons given above that is not the volume GA market.
I suspect as diesels improve they will replace Avgas engines, but I also suspect it is very unlikely turbines can be made cheap enough to offer a viable alternative for the majority.