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Is there a protocol limitation (I suspect there is) that does not enable transactions across different platforms to access a 3rd party remote server (Chaumian server?) through API and create a coinjoin every let's say 2 minutes or 100 users from all platforms/wallets? If someone implemented such a server, this would highly increase coinjoin liquidity and privacy.
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There is nothing in particular stopping exchanges from using CoinJoin to construct transactions with other exchanges, but rather there does not appear to be any demand for this. For example both JoinMarket and Wasabi1 have APIs that could be used.
In the future this situation could change if something like Schnorr signature aggregation capabilities are adopted by Bitcoin. In that situation, CoinJoin transactions could be noticeably smaller (and therefore cheaper) than many separate single-output transactions. This still seems very unlikely though as the exchanges are more likely to simply batch their own transactions rather than working with other exchanges.
Until a significant percentage of users demand privacy, exchanges are unlikely to change anything. There may also be regulatory issues with them providing such an option.
