This is just because people have more permissive public profiles than default. I view this as a privacy feature for people who may want to be on LinkedIn but only use the site to communicate with their connections - if they have a limited/empty public profile, then you won't see any additional information.

Yeah, I agree they should probably check and see if the public profiles are more permissive than just the top bit of information, but I imagine something about their architecture makes that difficult.

I also agree with the point about the NYT paywall; it's likely just a tiny additional monetization strategy.