I love the books and I think these movies were so well received was they were not terrible and by and large stayed pretty faithful to the source material.
Looking back now, the best thing about the movies was the fantastic score.
Personal taste is personal taste but this is a hell of a take. Like saying Star Wars was well received because people in the 70's wanted a big budget movie that was fun rather than depressing for once. They're films with huge casts and a vast back story that never kept you wondering about who was who or why they were doing something, filled with amazing action set pieces and acting that's almost universally excellent. It would have been so easy for them to be silly it's practically a miracle they succeeded at all, let alone on the scale they did.
The LOTR trilogy was groundbreaking - the first films ever to be filmed as a trilogy and as blockbusters without a star, based on a property thought to be unfilmable and only for nerds. It changed the face of big-budget filmmaking, showing it was possible to produce a serious and large-scale adaptation of a fictional property without dumbing down for a mass audience. Without it you don't get the Nolan Batman films, the Marvel cinematic universe or Game of Thrones, just more along the lines of Batman Forever, the Burton Planet of the Apes and occasionally the Matrix sequels, forever and ever amen.
In a wider sense, it was arguably the biggest factor in the switch from the jock culture of the late 90's to the geek-friendly culture of the 2000's (along with the emergence of the Neptunes and NERD in the music world). The response to it was off the scale from practically everyone, not just fans of the book, who were relatively tiny in number anyway. I've barely ever seen anything in the cinema that's blown me away like this did.