I do not think this should be a trading vehicle, thus I suppose each mint can make up their own rules. However down the line with a liquid derivatives market one could potentially manage a more sophisticated mint.

However answering to individuals need of a less volatile medium of exchange is a use case and should have a price. Thus the mint could simply transfer the exchange rate risk upon to the user, meaning if btc price moves, the cost of exiting would be upon the currency holder and the benefits equally goes to the mint for its longevity and sustainability.

BTC price down -> user gets entry amount of sats

BTC price up -> mint gets entry-exit sats.

A model like this would also give interesting possibilities for mints as revenue vehicles.