Due to recent events with mixer being confiscated by authorities, or mixer doing an exit scam, or with a seemingly legitimate pro-privacy company going in the opposite direction, I think a clarification of where we are at the moment in protecting the users' privacy is necessary.

There are three ways to secure privacy of your bitcoins, each of which comes with its own advantages and disadvantages. Pick according to what fits you best.

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.