FHFA offers to let Treasury convert its senior preferred shares to zero-dividend, non-cumulative preferred shares with stated value equal to the senior pref liquidation preference (currently around $273B for FnF combined) that automatically convert to a total of around a trillion common shares (not adjusted for a reverse split) upon sale to an outside party.
Treasury accepts, giving it essentially 99.9% of the common share base without having to worry about majority shareholder or balance sheet consolidation rules.
What stops Treasury from doing this to the juniors is the juniors' contract rights. Preferred shares can't be diluted, common shares can.
It's less about trying to take out current common shareholders and more about capturing all the common share value for Treasury rather than unnecessarily leaving any of it behind.
Wrong. All that says is Treasury does not have the right to convert the seniors. That language neither prevents FHFA from offering a conversion to Treasury nor Treasury from accepting it.
You might want to read further in the very document you linked to. Section 10(g)(ii) on page 7:
This means that the Companies, at the direction of FnF as conservator, can make an agreement with Treasury to amend these stock certificates at any time. So even if Section 6 somehow did prevent a conversion (which it doesn't, because you clearly don't understand what a "right" is), it could be amended away if FHFA and Treasury agree.