Right now, UST makes up nearly 2% of total stablecoin market cap. Yet, it is has all the potential to gobble up a lot of more in the near future. Apart from all the promising new projects on Terra that use UST, UST taking over more of the stablecoin market could spike $LUNA prices even more.
Since most stablecoins ($USDC, $USDT, ...) are collateralisied by centralised assets (USD, Gold, commercial paper, bonds, ...) the SEC wants to treat these coins as securities. Banks are seeing the outflow from their reserves to DeFi and are putting pressure to regulate these "securities" and subject them to US law. As of July the SEC are digging into the issue more seriously and it is a matter of time before they take actions. Whereas $DAI is somewhat more decentralised, 69% is still backed with $USDC (and 29% with $ETH). If $USDC gets regulation $DAI will be affected too. UST is still the most decentralised stablecoin out there. Which is also the reason why American exchanges don't trade it.
Terra's UST isn't backed by any collateral, instead it is arbitraged by burning/minting $LUNA. And since Terra is based in South Korea US law isn't applicable anyways. If Korea start to crack down on them (which would be an unwise move, considering their current/potential scale as a company) Terra will just pack up and start writing code somewhere else. Even though financial institutions don't like it, legally there isn't much they can do. Terra's Thai Baht stablecoin is still being used, even though the Thai government tried to crack down on it. After all it's just pegged to the value of THB, and not backed by any Thai funds.
After Col-5 goes live, UST will become the main stablecoin for the IBC on Cosmos ($ATOM) and it will move around freely between more and more blockchains. I wouldn't be surprised if it becomes the biggest one on $SOL in a matter of months and the largest one in DeFi over time as fear of stablecoin regulation grows.