You are right about this. I know people talk about risk of CEX every day. "Not your keys, not your coins" that is true and on DEX you don't have your keys.
In DEX you
do have your keys.
However, if you are choosing a big and trusted CEX, at least you are safe somewhat.
Or you feel you're somewhat safe, but you're actually highly exposed. All this personal information, name(s), selfies, credit cards, bank transactions, drivers license, passports, physical address, other biometric data etc., encourage your identity theft. You're giving enough information to a stranger, who's provably going to sell it to other third parties or get hacked leaving all of your info to the black market. Now lots of other strangers, with worse intentions, can impersonate you.
Whatever isn't private, isn't safe either.
So in this generation of DEX, it is not actually decentralized and because lack of regulations, it is risky to trade on DEX (rug pull). It's just my opinion.
I don't know what's CryptoBridge that you've mentioned, but there are, indeed, completely decentralized exchanges. The most reputable?
Bisq.
DEX is not really decentralized if the founder, owner are all well known. Government can knock their doors and force them to do KYC or shut down their DEX anytime. Nowadays, it is super rarely to see a project initiated by anonymous team.
That's true if the founder can control the DEX, which essentially means that it's not really decentralized. But, for a non-controllable and libre software like Bisq, it's considered decentralized. Same as with Bitcoin Core.