Uncle Sam shouldn't own Intel stock

The problem is that these days they do it capriciously, without any sort of plan or intention.

The government played a foundational role in supporting the early stage research that enabled companies like Intel to emerge. Underwriting that sort of long-term investment that wouldn't easily attract commercial capital is a great place for them to be.

Meanwhile, is it even the case that the American chip industry is declining? Apple, Nvidia, and Google all have significant chip manufacturing operations. And this isn't an industry I even follow particularly closesly.

No, they all (as well as AMD) all have significant chip designing operations. Not one of them can actually fabricate their own chips. Every single one of them must speak to TSMC or Samsung if they want to take their designs from the whiteboard to the physical world.