I think what Google+ got wrong is that connections are a 2-way street, you may not realize your new friend _wants_ the day-to-day updates and soccer game invites, because to you they may just be someone you met at work.
Imagine if you could have a list of feeds to follow, personal, professional, etc. And when adding someone you could follow whichever feeds you wanted, and unfollow certain ones at any point. Some could be private, so you'd have to be approved to follow.
Then I wouldn't feel the need to remove old acquaintances from fb, I would just unfollow their feeds. I would feel comfortable posting stuff related to my job/networking because I know only people following my professional feed would see it. And I'd be comfortable posting personal stuff to my personal feed if it was locked and I was the maintainer of who could follow it.
They could pretty easily implement this in facebook and I could imagine it breathing life back into the platform.