A national security investigation into Musk purchasing Twitter, or any of his business dealings, has huge negative implications for the US and would get the US government in very hot water.
SpaceX is one of the five most strategically important national security players in the US, and even globally.
I mean Musk calling a press conference (or more likely Tweeting) that if the Biden Administration doesn't trust him with Twitter then he doesn't see why they should trust him with NRO satellite launches and so SpaceX is temporarily placing all of its government launch contracts on hold would cause the entire NatSec establishment and Congress to explode on the Biden administration basically instantly.
Just investigating him purchasing Twitter on NatSec grounds would cause the Republicans, especially if they take the House or Senate in the Midterms, to open up all manner of Congressional investigations into the Biden administration.
An American citizen with TS/SCI clearance and, by dollar value, the single most valuable government contractor (as an individual) purchasing an ultimately relatively small website is a threat to national security?
It's a claim that just doesn't pass the smell test, which means really easy political hay.