What is your concern about giving your ID to LinkedIn? You mention leaks of IDs, but is that the primary reason? If leaks, what is the worst case scenario?

For me, I think of privacy in terms of other people not knowing my business, not knowing thoughts or activities I don't want them to, and not trying to unduly influence me, especially using information they may have learned about me.

LinkedIn is inherently about sharing information about yourself publicly. It's saying, "Hey, I'm {name} and I'm a {type of profession} and here are the types of work I've done previously." So to me, having to give LinkedIn my id isn't much more of a risk than the endeavor of using LinkedIn anyways. It's giving away a little personal information in order to gain personal benefit.

I've found it to be worthwhile. Since a little over ten years ago I've changed jobs twice and both were from headhunters contacting me. I've also spoke to a handful of other potential employers via headhunters. I don't think they would have found me if it weren't for my profile. So I'd say go for it.

Also for what it's worth, I don't think the "ban" is because they object to a VPN so much as people are constantly trying to create fake profiles. Asking for ID is a way to fend off inauthentic users.

Lastly, if you're not already, I'd strongly recommend participating in a professional association. Despite potential awkwardness of talking with strangers, connecting with someone face to face is a much more effective way of finding work than sending applications out into the void. You're a real person to someone when face to face and participating in activities, instead of an email that can be ignored. In the group I belong to I've seen multiple people show up looking for work and find it.