For the same reason the government bailed out the banks, they're too big to fail.
Two companies account for most of the frontier R&D, and something like 7 companies account for a huge portion of growth in the stock market. The government, especially under Trump, is very focused on continuing to see those numbers go up.
I also expect the government is pretty bought in on AI being the future and on us being in a race with China. They'd have to bail out the labs for those reasons alone.
Lastly in my opinion, Trump has a pretty socialist bent to him and regularly talks about a sovereign wealth fund owning portions of companies. He'd love to have take a partial stake in AI companies, and a bail out is a great way to do that.