This idea that people may come up with any contract, and it is the State's duty to uphold it, is baffling. So the state must use violence to enforce any agreement that might be written down between two people? Of course it is the State's prerogative to decide what it is willing to enforce and what it won't. I wouldn't enforce non-compete agreements either, simply because I think the world will become more interesting if such agreements become moot.
Discussion
What recourse would a person have if one party fails to uphold a written contract? Upholding binding contracts is a basic function of a civil government, as it is a matter of justice.
That said, I think forbidding non-compete agreements is a net good, because it removes coercive tools employers can use to disrupt open and fair competition in the job market.
That word "binding", what does it mean?
When I call a contract "binding," I mean that the parties involved have obligated themselves to fulfill the agreed terms of a contract.
Once such a contract is made, failure by one party to fulfill it would be an offense against justice. When an one party fails to act justly, the wronged party must be able to take recourse to some legitimate authority to ensure the demands of justice are met. Oftentimes, that would be a judge of a civil court.
Who is going to run a service that figures out and enforces any contract without limit? That would be like having a blockchain without any block size limit.
No one needs to run such a service all the time. All that is needed is an authority to which the wronged party can take recourse when another party has broken a contract.
That's why courts of law were invented.