The movie does not detract from the book in any way.
I disagree with this. Like I said before, it seems to me like when books get film adaptations, the film tends to supercede the book's cultural legacy.
I'm a bit undecided on this. I first read LOTR almost 10 years before Fellowship came out, it was also pretty much the first fantasy book I read, so I don't feel the movie supercedes the books for
me. Visually a bit maybe, but then I liked the visuals a lot and they were heavily based on existing illustrations and such, with some of the best Tolkien illustrators involved in the production. The stuff I didn't like as much, like for example elves having single-edged blades, doesn't pop up in my head when I re-read the books.
Also Tolkien is such a classic - fantasy as we know it wouldn't exist without him - that his cultural legacy is way too important to be forgotten.
On the other hand there are a huge amount of people who discovered the books through the films and an even bigger amount who has just seen the films (and probably would never have read the books in the first place.) Before the films came out, a lot of people I know had not read the books or only heard of them. So yeah, it might very well be that the films supercede the books in public memory. Public memory is also very short-time, there are many many books that used to be very popular and are now just "cult classics", known only to people who are deeply into that genre.
For example, recently someone mentioned Elric of Melniboné in another thread. That series was hugely popular a few decades ago, with RPGs and everything, but I think it has become a bit forgotten, with the promised movie never appearing. It's not as important a classic as LOTR, but still was influential at it's time. There is also stuff like Conan, which would probably be forgotten without the 80s movies.