Doing a bit of research, it looks as though there is no particularly good reason why there shouldn't be small turbines. The ones they were developing for cars were lower tech than your RR Trent but still produced OK mpg. They fell out of favour because of problems with accelerator response and large amounts of hot gasses being vented. Also turbines like to be run fairly flat-out - alright for pressurised air liners but not so good for pottering around sub-10000 feet. The real reason is probably the same as why such old/low tech Lycomings and Continentals have lingered for such a long time. There seems to be a major barrier to introducing anything new.