There's still plenty of exchanges that don't require any form of documentation for "Know Your Customer" regulations if you're dealing with crypto-only transactions.
Might sound odd but almost no country has come up with a full framework for crypto regulation, let alone fully enforcing it. For instance, even people from the U.S. can access most Chinese exchanges to this day, and exchange crypto-to-crypto without passing any checks.

Think about it, any top-10 exchange will have billions worth of BTC circulated through its systems every month. Yes, the receiving parties will be able to trace that the BTC might have passed through the exchange, but the origin of these funds is going to be as obscure as possible.

Compared to the average mixer, that circulates at best a few thousand BTC at any given time, no matter how much a mixer tries, it'll never be able to be as obscure about origin and "cleanness" of funds. Hell, even North Korea's Lazarous group is known to be laundering tons and tons of money they hacked from DeFi through no-KYC exchanges.

If OP here had made a single pass-through from a no-KYC exchange there's no way Uphold would have detected him. On the contrary, the mixer got detected in spite of all its efforts and hefty fee.
To think that Uphold, being as incompetent as they are, has systems in place to detect mixers, it's sure as hell is pretty rudimentary to detect such transactions except if the mixing service is exceptional at what it's doing and also has clean coins at hand. Which I doubt they would just hand over to any run in the mill customer doing small transactions like that.