In the world of crypto, where people keep repeating the "not your keys, not your coins" mantra, crypto exchanges are very much the owners of all the coins they hold. But I agree, it's absurd.
Would you trust an exchange name "Uncle Vlad's Russki Crypto Exchange"? Probably not, right? Because if they take your money, and you call the Russian version of the FBI, they'll just laugh at you. So you think your money is safer in a crypto exchange where the founders would be arrested if they blatantly stole your money...
People seem to conflate "it works like physical cash but it's electronic" with "no banks no laws no regulation" when its very obvious that banks and governance are still necessary.