It is interesting to me that there is any substantial demand for a Tether, when $1 is always worth $1. If Tethers are actually worth $1, why not convert them to dollars and avoid the counterparty risk entirely?
Tether should only be issued based on the amount of USD that Tether has in its bank account / vaults (they have released a 'audit' by a law firm but not by an official auditor). Since each Tether represents exactly $1, market forces should handle the pegging. Assuming people trust that Tether does have the USD, then any price < or > $1 represents an arbitrage opportunity.
The demand for Tether comes from the fact that many exchanges are not licensed to operate in USD. Tether is used in place of USD on those exchanges, and the counterparty risk you mention is likely balanced by arbitrage opportunity.
It's not clear if tether can really be "redeemed".
The price of tether will likely never reach 1.1 unless there are solvency concerns. Any price disparity between BtC/usdt and BTC/USD has historically disappeared, so you can pseudo-arbitrage these pairs across exchanges even though they are technically not the same. Kraken's USD/USDT pair also makes this bridge easier.
Secondly, AFAIK many exchanges including Bitfinex had trouble letting people withdraw USD. I am not entirely sure if that has changed recently.
So, in both cases Tether acts as a counterparty to BTC trades. In most cases, the BTC/USD pair is not actual USD but TUSD.
But in practice I don’t know enough to be confident that a tether is always going to be $1.