Mouthwash is like handsanitizer/disinfectant spray, yes it may kill on a wide spectrum but the bad stuff does you more harm than the good stuff does you good so net/net it's worth it. I don't use mouthwash very often and tbh I can't really see the point in it due to the low fluoride concentration, there are maybe some corner cases where it's useful but not for me. PS the NHS article you quote concludes
There is certainly no credible evidence that mouthwash "can give you cancer".
You don't really need science to back up the link between poor oral hygiene and tooth loss through perio problems, there are millions of cases walking around today but even applying some basic logic shows the truth of it.
Imagine your knife gets wet (plaque) and you don't clean and dry and lube it, it'll eventually develop into rust (calculus/tartar) Now assume just a tiny bit of water gets under the scales and develops into rust which expands the gap then more water (plaque) collects in there cos is easy to get in and hard to dry (clean) which then rusts some more, expands and eventually the scales fall off/become loose as heck. If you can't get to the rust to clean it out, the knife is pretty much doomed in the long term. It's the same mechanism. It's a very simple analogy and doesn't take into account the bodies immune response (makes things worse through swelling) and healing ability (wish my knives did that!) but the basics are the same.
Also you say dental care has become exempt from NHS services, why do you say that (I'm interested as my wife has been an NHS dentist for the last 30 years and I'm wondering who's paying her wages...) and
https://www.nhs.uk/using-the-nhs/nhs-services/dentists/
However I do agree with you in that a dentist is like a car mechanic, a doctor, a plumber or anyone else providing a service, you should always make efforts to understand the options they offer you, the cost, the implications etc Do shop around and find one you like and trust (I still to go the same mechanic even though I moved away from him 22 years ago!) Most Doctors and Dentists can be trusted they don't intentionally proscribe bad treatment for you as they will need to pick up the pieces if it goes wrong but there are always options for you to choose from and most dentists would rather not see you ever than have you back and in pain every week (bad PR and the don't get paid for fixing problems they already should have fixed)
As another genuine question what are your thoughts on vaccinations?