But what ultimately matters when remixing is the new coins that come in. If you do a coinjoin with all inputs remixed, then it won't make a difference. Also, it makes yourself more untraceable to be in a coinjoin with 100 inputs, than in one with 5, so the number of inputs used surely matters.
Absolutely agree, but my point is the size of the total liquidity pool is not that relevant because nobody is mixing with every other output in the pool. Whether the total liquidity is 5 BTC or 500,000 BTC, it doesn't make a difference if I only coinjoin with 0.5 BTC of it.
So let's say JoinMarket has ~700 BTC in liquidity and Whirlpool has ~8,500. I have 0.5 BTC to coinjoin in each one. For JoinMarket, I perform a single coinjoin with 19 other participants. For Whirlpool, I perform a single coinjoin with 4 other participants. At this point, my anonymity set is greater for the JoinMarket, even though Whirlpool has the greater overall liquidity. But then I leave my coinjoined output in Whirlpool and it gets another 5 free remixes. Now my Whirlpool anonymity set is exponentially larger than my JoinMarket one, especially once you consider the forward looking anonymity set and all the free remixes that every other output I have coinjoined alongside is also getting.
I guess the essence of what I'm saying is that liquidity is not the same as anonymity set. It is difficult to say which out of JoinMarket and Whirlpool provides the best anonymity set, because it depends entirely on how you use them.
What's important here is to break down what's user's best courses to accomplish mixing. Even if funding blockchain surveillance is completely contradictory to being proclaimed a pro-privacy service, that doesn't change their coinjoin process.
It absolutely does. Any sane user of a privacy service does not want the fee they pay being handed to blockchain analysis to spy on their inputs and potentially censor those inputs based on their findings. This is antithetical to the entire concept of privacy.