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I think you mean you can't transmit cash between crypto exchanges. You can definitely transfer them into exchanges. Or perhaps you meant you can't store in a hardware wallet.

I personally don't believe any of these things make the case for holding a stable coin.

Remember the coin is pegged to a real thing, so it can't outperform, but it is at risk of total collapse. The only way for the "cash" you hold to collapse is for the entire banking system to collapse. In which case, you're still better off holding BTC.

They all never fail to redeem, until one day they do.

Then how does the cash get into Tether?