They did come about, in the late 60s. Williams worked on these to varying degrees of success. One of their designs became quite famous. The F107 powers the BGM-109 Tomahawk and AGM-86 ALCM.

https://www.smithsonianmag.com/air-space-magazine/the-little...

There are companies that have tried, like Capstone (formerly Capstone Turbine, then Capstone Green Energy). Capstone declared chapter 11 bankruptcy last year (since emerged and continuing under new leadership.)

I still believe it's possible - for example by having all the blades enclosed in a ring you can avoid gas escaping 'round' the blade.

And with metal 3d printers rapidly falling in price, I think it will get within the scope of university students to prototype soonish.

Fun fact, before the oil crisis the French TGV was originally a gas turbine train.

They definitely exist for small RC aircraft, but they're very expensive.