Question. I've used phosphoric acid to clean stationary parts but where there is movement and substantial load bearing involved, as with a vise screw and nut, how does the "rust converted to ferric phosphate" react?
It rinses right off the steel. It turns into an aqueous ion and no longer remains attached to the steel. Once you wash the steel down, it will be bare steel and will flash rust.
There is no fundamental chemical change to the metal. No reduction in strength. Nothing. This is a surface reaction.
Note: If the part's dimensions change because it was mostly rusted through, of course its strength is compromised. But this is no different than what happens if you use a stainless wire brush or electrolytic rust removal.
Note: Do not leave the part in the phosphoric acid for days. This is not weak sauce electrolytic rust removal. The acid will etch the steel as it oxidizes in the water after the rust is gone.. It is slow, but it will happen. I have left steel parts in a phosphoric acid solution for a week and there was severe dimensional change.