When you put money in the bank, it's backed by 1% real assets (go fractional reserve money!)

So let's say I don't want to put my money into something that is only 1% backed (See the Greek dept crisis). I could store cash under my mattress, but that also has some major risks.

With a stablecoin like UST, you 100% own it. Governments can't confiscate it. It's 100% backed by the asset behind it (not talking about Tether here ;)). I do agree that it comes with its own set of risks, but some people might prefer that risk over the ones above.

Or maybe I'm a foreigner and want to keep some of my personal value in dollars, but don't want to do that in cash or at some local bank.

It's basically another option at your disposal. And as the market cap of those stable coins prove, lots of people prefer that.