Gas turbines are not very fuel efficient.
The argument about fewer moving parts is often made. But generally turbines are more expensive to make. They require precision engineering. Whereas regular engines (if you've ever worked on one) don't require that nearly as much.
I appreciate this if it's for turbochargers, but turbines share many similarities with them.
https://www.youtube.com/watch?v=-bZu8atQ8lY
BTW, Garett builds/rebuilds turbochargers in many vehicles. If you have a vehicle with a turbo, see if it says 'Garett' on the side.
A turbocharger (compressor) is already about half of a typical Brayton cycle. The power turbine itself can also be radial in design.
Unless you need insane mass flow rates, radial is probably superior to axial.
Brayton cycle does not necessitate a free flowing jet engine style design.