LinkedIn is not a public service, LinkedIn is a private, for-profit business. A public service is normally publicly funded. https://en.wikipedia.org/wiki/Public_service
> with the intent to your users that such information will be available publicly, you cannot then police what users of that data you consider to be "public" because it serves your business interest.
LinkedIn licenses their service to both free and paid users, and they can legally and do attempt to police what users can access the information. Whether it's enforceable or not, LinkedIn has a EULA and use of their service, whether you have an account or not, is presumably governed by their license.
They are well within their right to restrict requests being made by spammers and DDOS attacks, for example. How do you tell between legitimate requests and abusive ones, and how could you compel public access without enabling abusive ones?
> LinkedIn, of course, wants to get all the benefit of the public Internet with providing as little as they can.
The internet isn't a public service yet either, at least in the US. I think it should be, but it currently is not. This is conflating the knowledge that everyone with a computer and net access can currently access a LinkedIn server with the idea that everyone must be able to.