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> Even backing a currency with gold (or any other asset) doesn't solve this problem

It actually does. If the backing is real, the user knows he will always be able to exchange his coin for $1. If the price on an exchange goes under $1, the issuer of the coin can buy it back, making a profit. If the price goes above $1, the issuer can sell. It's a trivial algorithm. Of course, it only works if the backing is real.

Unfortunately having billions in cash is a huge temptation to invest them and make even more profit. That's what Tether did. And now, if their commercial paper is under water, they are insolvent.