Contracts like that are frequently unenforceable in the US. A no-hire provision is not a provision you agreed to, and yet it binds you. Courts take a dim view of this sort of restraint on trade.
This is right. Sure they can hire the new person but they are immediately in breach of the services contract. Sometimes the breach is with it.
The non solicitation clauses are not about stifling employee personal growth. They are about protecting the organization from having its resources pillaged. It’s a reasonable protective instrument in my view.
The two companies may have an mutual understanding whereby they do not take each others employees to maintain the peace. Even if not enforceable...it may create friction when trying to move over..