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.

And chew through fuel at truly extraordinary rates.

This one, for example, weighs 450 grams, but can consume its own mass in fuel every three minutes!

https://www.kingtechturbinesaustralia.com.au/product-page/k4...