I don't know exactly how it works, I believe Prime needs oxygen to oxidize (it is a reducer, right?). How much oxygen? Good question! Nitrification itself require oxygen since NH3 is converted to NO3, right? Do you conclude that nitrification is a bad process because oxygen is needed?
"It would take a massive overdose to have any effect on the oxygen levels in the tank" according to Seachem T
I'm glad seachem and you agree that prime and other ammonia locks dechlor do in fact lock up oxygen.
And I'm sure you have read MSDS's on other products with sulfide compounds which state they are not to be released on streams and lakes as they kill fish and present a danger to aquatic life.
So now the only questions is whether or not adding these chemimcals to tanks is better then adding plants which do exactly the opposite. After all I have nevere heard of thriving plants killing fish.