No a cease and desist doesn’t require a lawsuit, where does that apply? You have your lawyer draft a letter and if they ignore it, than you have to go to court and deal with it, but these aren’t used frivolously like DMCAs so they are usually followed.
You can’t DMCA something that isn’t copyright infringement, if you’re hosting it yourself, a DMCA doesn’t even really apply to you either. It’s for third party hosters. And you still need proof regardless, you can’t just dmca stuff and not follow through with proof and enforcement.
Your point is inherently flawed it seems.