So large skyscrapers, large nuclear plants, datacenters, etc would be state owned. Actually more…. This would be hundreds of the largest companies. This means the state would commandeer a company when what, the market cap hit a billy? The nav? That actually seems kinda crazy to do

Not state-owned, just state-managed. We already generally subsidize power plants, but for other large projects it could provide both funding and oversight of the build.

When it comes to really large companies themselves, if there’s a cap then they would just stop being such large companies, not be taken over.

But if you wanted to make a process for a company to grow beyond the $1B cap, my personal preference would be a system where depending on the level of impact to peoples’ lives, either something like monthly auditing of financials and business plans, or for companies operating in areas with a higher potential for harms, something closer to a Fannie Mae-style conservatorship, that would directly advise the company on minimizing risks (and potentially actually prohibit actions outright if they clearly were harmful). Ownership, stocks, profit, etc, would all still be private. We actually already embed IRS auditors in companies if they’re caught doing tax evasion, and I think of this more as a logical extension of that. We’ve tried voluntary compliance with laws and regulations, and too many of the very large companies are happy to flout them, and use their wealth to help them do so.