I fear you may be correct.
However, I'm trying a thing......
I've connected a hose pipe to the tap (warm) and plonked it in the bath at the non-tap end and dislodged the plug at the other end slightly so that it is draining about the same speed at which it is filling.
So the bath remains full, and the flag soaking wet, but the water is gradually being replaced. It is getting less red, though whether or not it will ever get to be a usable white seems unlikely.
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