You are ezposing yourself to many risks: smartcontract risk (a bug may lead to losses), token risk (stable coins or wrapped btc might no be pegged ) or even a scam.
But in even in these cases, you do not have control of your own coins. As you point out, you have to deposit them to a smart contract address, swap them for a pegged token, wrap them on another chain, and so on. In all of these cases, you no longer own bitcoin in your wallet which you can spend as you like. You only have to take a look at the ICO craze to see just how many coins or tokens had either accidental or deliberate fatal bugs in them, which led to the coin either collapsing or the owner using it to scam. My favorite example was a coin called Oyster Pearl (PRL), which was shilled heavily on the altcoin boards, on Reddit, on Twitter, etc., and peaked with a market cap of $200 million. Then the creator activated a piece of code which no one had noticed which allowed him to print 3 million brand new tokens out of thin air, gave them to himself, dumped them all immediately, and ran off with the profits.
Any time you wrap your bitcoin, or swap it for a token, or deposit it to smart contract, etc., you assume a similar risk.
Anyway, I don't think this is something to worry about if you can prove you bought the coins after it was mixed when the exchange asks you about the source of your funds.
First of all, why should I have to prove where my coins came from? The whole point of bitcoin is to not trust centralized third parties, not hand over your entire financial history on their every whim. Second of all, what if you can't prove it? What if I sold something to a friend or acquaintance for the bitcoin in question? Or what if I traded for them peer to peer directly with another person? No exchange history, no receipts, no screenshots, no bank statements, etc.
Exchanges should not be enforcing these completely arbitrary rules, and we should not be supporting exchanges which do.