i would emphasize that you cannot lump coinbase together with all exchanges. many exchanges will do no such thing.
Absolutely. Allow me to elaborate:
Coinbase and other exchanges will track coins backwards and forwards multiple transactions.
Pretty much all exchanges are tracking your deposits back multiple transactions and your withdrawals forward multiple transactions. They do this to ensure they are complying with AML regulations, funds aren't arriving from or being sent to illegal darknet markets, etc. Whereas (emphasis added):
If you are using an exchange which looks down on gambling and casinos
Some like Coinbase also lump things like mixers, casinos, sportsbooks, and as you say, coinjoin transaction, in to the list of "unsavory" things that they do not permit their customers to spend their own money on.
i would much rather own clean outputs withdrawn from an exchange than coinjoin-linked outputs---at least until bitcoin privacy is improved enough to obfuscate coinjoins.
Genuinely question - where are you sending or spending your bitcoin that you need "clean" outputs? I have used various mixers in the past, including ChipMixer a lot, and have started to use some coinjoining as well. I have never once encountered a problem spending my "tainted" coins, but I also don't use centralized exchanges at all.