Not only you can. You also should. And for a very ugly reasons.
Now, a disclaimer first - according to my own experience and unanimously everybody among my acquaintances, it's never'ish to your benefit and I'm in advance apologizing for the rant-like statement.
Your profile is a valuable resource to recruiters. The number of CVs then "own" is a markettable gold. Especially if they present the portfolio of available, skilled professionals they have personal contact with. Many recruiters get paid by the profiles presented and it's simply cheaper to shoot from a pre-set cannon of applicants than contacting them to ask if it's OK to present them.
What about FOMO? Won't we miss on great opportunities because we're not readily set to be presented? Well... If you're so average and not in demand that you'll be missing out, then it's very likely that the employer won't hire you anyway. If you've got some (even modest) skills, you will be in demand. They will look you up. They will get back to you. There's usually hefty bonus if a candidate presented, actually turns out any good (and available at a acceptable price).
Also, be sure that most of the recruiters are desperate to get clients (employers who will hire) and it's a very competitive world (too many people shoving CVs back and forth, which requires very little knowledge). It means that their key selling point is that they can get good candidates cheaply. Let me translate it to candidatish: they will pay you less.
And show me the recruiter who will work hard so that you can get a good offer. There's a risk of annoying the client who pays them. There's risk of getting undercut by a competitor. You and your CV is just a merchandise and the lower they sell you to a job you'll soon get fired or tired from, the better. Being stored as a reject tell the reader that at least once and for some reason you were not interesting. Bad start...
Recruiters are not agents. They are something else that can't be stated here due to policy of professional language.
Oh, and asking, urging or even angrily, repeatedly demanding to be removed doesn't ensure that it will happen. You can get into a DB without your consent (because how would you know about it, right? and they can simply "happen" to have IT issue and by mistake "forget" to remove your profile. They can't because that's illegal? Well... so is rape and murder. Are you familiar with the concept of courts and prisons? There's a reason they exist.
There are good recruiters. There are also winning lottery tickets...
I'm immensely sorry and apologize to anybody who may have taken offense, felt insulted or unfairly described. I promise it wasn't you I referred to and I'm utterly happy that you do exist.