Uncle Sam shouldn't own Intel stock

The problem here isn't that the government gets involved in businesses. That has always been something they do.

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.

Exactly, and indirectly supported all business, with roads, the police, schools...

Government should own a stake in every business, and citizens should then get shares in that government fund.

I think that stake is called taxes. As for the shares, they're supposed to come in the form of government services.