As far as I know (IANAL) it is in fact the only "person" you can charge. To the best of my knowledge, the whole point these "limited liability" legal constructions exist in the first place, is to protect individuals within a corporation for whatever they do as part of the business of a company (barring exceptions that have clearly not been part of that business and obvious individually committed crimes), typically "just following orders". If a company commits a crime, or in a worse case runs a criminal enterprise, it is the company that is legally responsible, not its employees. That is, in principle.

This can get more complicated higher up the management tree, where decisions can also be prosecuted on personal little, but that's usually a far more complicated matter. Also, if a whole group of employees willingly conspires to commit crimes, they might also be prosecuted individually for those crimes (there are limits to limited liabilities). However, that usually only works under special conditions and it would e.g. require that there's an obvious criminal enterprise aspect to it, rather than individual cases of illegal conduct.

That said, with the track record of some of these companies, actually designating some of the AI companies as a criminal enterprises may eventually happen (in due time) in some jurisdictions outside the USA. Certainly if it ever turns out that these companies have been storing and (ab)using everything they ever had access too, while blatantly lying about that just because some particular (post 9/11) US laws gives them that opportunity (and impunity) as long as the US government somehow requested them to do so (covertly; with gag order). Might legally work withing US jurisdiction, but would still be very much illegal everywhere else.