>could we make a 2 inch diameter turbine engine reliably

I mean, technically yes, but in practical terms, no - turbines run on the Brayton cycle, where the are under curve efficiency is determined by the peak pressures it can withstand. if you scale down the turbine proportionally, it gets structurally weaker, meaning its efficiency drops. thrust/weight decreases

If you then thickened its walls you would then be able to handle higher pressures, but weight would increase - thrust/weight decreases again.

So the correct answer is if you really wanted to make a small turbine, you could certainly make one, but your design would be less optimal than a bigger one, so unless your goal is to go small, you would make one as big as you can get away with it.