Let's take your post at heart, and we'll ignore the part about phishing (ironic, considering your own site's setup).
Your assertion is mostly paranoia, what could happen, and what LinkedIn shouldn't do. LinkedIn should not ask for your email password, despite that being a way to access email. Now, I'm not suggesting you hand over your email password without thought, but you do hand out your email password.
You hand out your email password to any email client you choose to use, with the hope that it doesn't share out that password to anyone else. After all, just as a LinkedIn employee could steal your password, so could a Google or Apple employee as well. I mean, Google even asks for the password to other email accounts if you want to use Gmail for non-Gmail accounts. And let's hope that no browser is tracking anything. It might be open source, but have you checked the source code?
Sounds crazy.
So leave LinkedIn. But really, it's a rant, and not even a good rant at that. And we didn't even talk about glass houses.