I don't personally use Linkedin so I can't really comment on how a federated alternative would work or be useful for professionals and networking.
What I will say is that paid/business-related and the general fediverse culture/design seems like oil and water. Especially the paid part. It simply won't take off unless there is a mass exodus of people from Linkedin (very unlikely). And even then, having multiple instances for something as focused on Linkedin doesn't seem viable. It's probably better off centralized and disconnected from a large network like the Fediverse, in my opinion.
The closest the fediverse can get to this is professionals using Mastodon or something in the same way they used Twitter before it imploded. Interesting idea though.
Do you guys think Elon would let me take his SpaceX Starship in a time machine back to 2021 so I could fly to Mars and survive?
No, I do not have $4 billion to pay for this endeavor, I'll just take out a loan and tell the bank its for a scientific breakthrough.