I don't get pelted with a ton of messages - maybe a dozen a month at most, and maybe 1/2 of them are actual ops I could be interested in/are applicable to my skillset. I've had several interviews which originated from a LI message - easily over a dozen, and I may have landed a job in the past this way (can't remember unfortunately). This is sharply contrasted with my experience during the .com days upon graduating college - I would get 2-3 daily calls from recruiters for all sorts of things.
Unsure if it's because I'm older, more skilled, have a note that I'm busy on my LI intro, or what... but I have a relatively in demand skillset (Rails/React dev) and am getting messages for quality leads, even quite a few for remote gigs (I have a note that I prefer remote work).