Yes. This is called industrial policy, and there is bipartisan support for this. 2008 changed thinking on both sides of the aisle around leveraging state power to build industries.

Plenty of us Obama and Biden alums are industrial policy fans, and there is a similar cohort across the aisle.

The issues with this are precedent/slippery slope. Today it's a small stake in a small number of companies, but empirically government initiatives almost always grow. Once entrenched, I would be willing to bet that the government will take larger and larger stakes in a bigger and bigger number of companies until this model becomes a non-trivial, potentially dominant, share of the economy. I can see myself becoming a single-issue voter to oppose that future (although given bipartisan support I'm unlikely to have any options; maybe Rand Paul).

We desperately need a third party to displace one of these two. Having a state interest in industry is of course a great idea—telecoms, power generation, a base level of healthcare providers, pharmaceuticals, base level tech manufacturers are obvious things that should be state owned—but this just seems like an extension of the defense industry corruption (the "military industrial complex") that's plagued our country for many decades. Why am I paying to protect myself from china? Who will protect me from this one?

I'd be curious as to how much the executives at these firms earn (whether it be through salary or equity or whatever else).

As long as we're socializing the gains just the same as we're socializing the losses (through taxpayer-funded bailouts), I have no problem.

That's unfortunately not been the reality through Obama, Trump and Biden policies.