You can just make a few hops (transactions) to other addresses you have, to make that mixing undetected by exchanges.
Any exchange is more than capable of looking back a few transactions to see where the coins have come from. A far better option is to stop using centralized exchanges which attack the very essence of bitcoin by treating it as non-fungible, and will spy on you and censor you if they don't like what they find.
There are now plenty of decentralized exchanges, marketplaces, merchants, services, and so forth, out there which do not spy on you and do not promote the provable nonsense that some coins are "tainted". Use them instead, and stop worrying about whether some faceless third party thinks your coins are naughty.
I think this is true for most situations.
If you want to trade a 20usd for an Amazon card, you can certainly use a p2p solution, or some merchant or whatever...
But for people who are heavily invested in bitcoin and want to trade high values, this is not feasible.
Would you dare trade 1 or 2 btc in a p2p? This is very risky, and an exit scam is a real possibility. Additionally, people who live in developing countries mostly don't have an USD/EUR account, which narrow a lot p2p possibilities.
On the other hand, trading 2, 3, or even 5 bitcoin is quite secure in the biggest centralized exchanges.
What is more ironical about "clean" bitcoins, is that some exchanges consider bitcoins "tainted" after a recent mixing process.
You can just make a few hops (transactions) to other addresses you have, to make that mixing undetected by exchanges.
If I remember it correctly, somebody said their mixed coins were classified as tainted even though they already move them through some addresses. So some exchanges might trace back to more than just one past transaction to see if your coins are "bad" or not. Although if you use a mixer that doesn't really make it hard for exchanges to see that you use them is a bad idea to begin with.
you can just do 4,5, 6 hops... It is quite cheap to make an on chain transaction with 1-2 sats bytes.