Thank you for your response - no matter how trusted a mixer is there are too many factors at stake that make it impossible and foolish at the same time to fully trust a service, even if the operator has the best intentions at heart there are still many things that can go wrong. I strongly believe there is nothing illegal, but there will always be risks and everyone has to understand and acknowledge this
Our model may sound relatively similar to Chipmixer, but it's really not. I believe that all mixers at this point in time have a very strong weakness, and that is the fact that in the case of Chipmixer even though you can spend your chips whenever you want like you said, they are funded a very short amount of time before your actual deposit, so an in-depth analysis by a firm with some resources could narrow down the possible deposits to a small enough range that it may become possible to identify where the funds came from. The fact that you know they are funded before kind of defeats the purpose
This is the case with others too, let's take Sinbad as another example. You can choose when to receive your funds between 0-168 hours after your deposit. Someone that knows where to look will be able to narrow down the possible deposits to a small list again.
And another example the type of mixer that has multiple clusters and sends you bitcoins from a cluster that has "nothing to do with your address". In reality that doesen't change anything since the clusters are known anyways so it may actually be worse to do it this way because then you are sure that the deposit was not in the cluster where the BTC came from, so again this is all information that could help track your funds.
I am not trying to disregard any of the services I gave as examples and I'm sorry if it comes out that way, they still achieve the desired goal for most users and the points I raised may be irrelevant for most, but it makes for an interesting discussion nonetheless
As much as people don't want to hear it "mixing" can't really break the link between your deposits/withdrawals 100%, the best it can do is obfuscate everything so much that it becomes impossible to prove someone's withdrawal originated from a specific address, and this is certainly achievable with a good system and patience.
Our way of achieving this is with the notes, but more specifically when you deposit your BTC goes into our main address together with all other funds and stays there until you decide to withdraw it. So for example you could deposit 1 BTC today, withdraw 0.2 BTC in a week, another 0.5 BTC in 3 weeks and the rest in another month. Or you could wait 3 weeks, deposit another note with 0.75 BTC , merge it with the one you already had into a 1.75 BTC Note and withdraw to 3 addresses 1.2BTC, 0.3BTC and 0.25BTC. The longer our service will run, the better the anonimity set will be. We have an initial reserve that will be available so users can mix their coins from the start, but after a while technically speaking EACH withdraw could originate from ANY deposit that was made from the beginning until that point. (instead of a ~200 hour range before or after the deposit transaction)
About the decentralized solution I don't think funding is the biggest issue since it could charge the same fees as a centralized solution and split them between the validators and that should probably make it worth it given the high volume that this service would presumably facilitate, so if it works it's all good. But at the moment I'm not too sure there is a big enough market to make it worth the time it would take to do it, but I will have more insight after a while of running the centralized solution.