The $n!$ conjecture is perhaps another near-miss. It was posed 25 years ago by Garsia and Haiman, and the ideas in the paper are interesting and non-trivial, but the conjecture itself was probably the most interesting part of the paper, and was a major stimulus for the next ten years until Haiman finally proved it.

Along similar lines, the shuffle conjecture was introduced in 2005 and recently proved by Carlsson and Mellit. The conjecture itself was the most interesting part of the original paper and it stimulated a lot of research.