Some new people you meet will prefer to see who you are by looking you up online. At least to me, someone's online presence is a testimony that the person is who they claim to be when it comes to their experience.

I’m the opposite, I think online profiles are completely untrustworthy and likely as not to be filled with exaggerations or outright lies. But I’m probably in the minority?

This shouldn't be an either/or thing. Any public facing profile, especially on a platform like LinkedIn which is large and has many eyes on it, is better than none if you're looking to get the word out. I've had a LinkedIn profile from nearly the beginning, and although I nearly never use it, I am occasionally contacted by people about work. If I spent even an iota of time filling out my profile and posting regularly, it would probably bring me many offers. (Whether they'd be what I'm looking for is another story.)

If I had to choose between a public facing profile or a broad in person network, I'd choose the in person network. But you really shouldn't discount the online profile, since it's free advertising for you.

I've been on Linkedin from the start and I don't think I've ever gotten work or meaningful benefit from it other than seeing what some acquaintances have been up to over the years and occasionally getting a message from an old friend reaching out to catch up personally.

It's a useful online Rolodex (to show my age). I've had a few recruiters reach out over the years but it's never been useful for that purpose beyond that.