I believe your "checkup" and their "routine cleaning" are the same thing.
Lots of people (myself included) refer to it as a "cleaning" because, well, regardless of anything else, that's what they actually do to you. I don't know anyone who goes to a dentist just to have them look but they don't touch. They clean you, too. That's almost always the only physical takeaway effect of one of these visits.
Also, a dentist cleans your teeth in a way you almost certainly can't. Their practiced hands know exactly what needs to be scraped away, and they can make informed decisions on what tool to do it with and how aggressively to not cause enamel damage. Not to mention they can, y'know, actually see what they're doing in there. So a "simple cleaning" isn't quite as pedestrian as it sounds. It's not something you can fully replicate by scraping around blindly with a metal pick in your mouth.
I admire the respect you have for those who ask questions like this, but I think I disagree.
If there is something egregiously wrong with the premise of what a person is seeking to do, and there are no qualifying statements in their query about why they do in fact need to do this specifiic thing in this specific way, chances are high that they are uneducated about why the premise of what they're trying to do is flawed, and they are best served by being course corrected. Giving them the answer they're looking for to continue the bad thing while hiding your suggestion of what they should be doing instead in a footnote is just enabling them to double down on the short term path of least resistance that will probably come back to bite them again later.
If they really did know what they were doing with regards to doing an otherwise unsafe and/or unsupported thing, or if the restrictions tied their hands from using the obvious replacement solution, it either should have appeared in their question prompt, or it should be in the first replies to the first round of answers.
I say, withhold outdated advice unless the context of the conversation makes it explicitly clear that the old advice is genuinely required and not substitutable with current advice. But also don't be smug, rude, dismissive, or standoffish about it. Don't argue with someone who says they really do need a specific solution.
That said, this only applies in really cut and dry cases like this one, where there very clearly is an indisputable thing you shouldn't be doing, and a drop-in replacement you should be using. The ones I hate are moreso those you may see on StackOverflow where the question is like, "how do I do in JavaScript?" and five of the seven responses including the accepted answer offer a solution in some big dumb framework or lib that they apparently expect you to just incorporate into your project.