Treasury doesn't want to own both companies. It wants to sell its stake in both companies to investors at a high profit. Just read Trump's famous letter.
1) Why would they ever do this? 2) Why would they do this instead of writing the seniors off? 3) Why would they do this instead of turning the cash NWS back on?
To which I would answer:
1) It allows Treasury to realize cash much sooner than ~2039 when FnF hit their capital requirements with the seniors still on the books and the above-full-capital-requirements cash NWS turns back on. 2) This one should be obvious. Writing the seniors off would be throwing a $220B asset in the trash can for nothing in return; converting them to common at least lets them recoup some of that value. 3) I don't have a definitive answer to this, but I believe one big reason is that it would fall afoul of the Supreme Court's denial of prospective relief to the Collins plaintiffs.
Because Treasury can only demand payment on the liquidation preference in the event of receivership or an actual liquidation. I'm not aware of anyone who sees either of those as a realistic possibility.
In essence the US government already owns both companies. FHFA provides the control, Treasury has rights to all their income ahead of current junior pref and common shareholders, and the "temporary" nature of conservatorship allows Treasury to refuse to consolidate FnF's balance sheets onto the government's.