I recently posed this question on r/history, and certainly received a lot of anecdotal confirmation of the practice of getting dentures at a young age. However, I'd like to read more about the subject and find out how common/where/when this practice was. I think the claim may actually be applied to late 19th to mid 20th century Britain, US, and Canada. The thought process ostensibly being that you could cut down on dental costs and toothache by just having all your teeth removed and getting dentures while you were young. The claim appears near the end of this article.
It's definitely not true. I've been putting off responding to this question because I wanted to at least be able to give you a substantial response, but this is not a subject where much is written. It must suffice to say that if this were considered the "perfect gift" for anyone, there would be some documentation.
Intriguingly, it's not even a question where I can find a lot of instances of the myth in pop history, so I don't quite know where the dentist quoted got it. I did find one reference in a more modern memoir to a hotel worker whose parents had done this in order not to pay for all of the fillings she needed, and another reference to an early twentieth century maid whose parents likewise agreed with her employer to do the same. Oh, yes - and in T. S. Eliot's The Waste Land, there is a section in which one woman tells her friend to have her teeth pulled and replaced with false ones, as her husband gave her money to do. In all these cases, this was done because the woman's teeth were already in extremely bad condition. I've never come across a reference to doing it preventatively to healthy teeth just in case.