I don't think 1st Amendment applies here since it's not the Gov imposing a no compete. Besides, in private business you sign the contract then those are the terms you agreed to, but there are limitations.How could a no compete even work, talking 1st amendment here.
I don't think any of this applies to Tucker anyway since Fox terminated the contract.
I read somewhere that Tucker had retained a lawyer. I assume they are going through his contract with a fine tooth comb, potentially for a lawsuit for damages if Fox acted without cause and to advise Tucker of any contractual limitations.
I think we may not hear a lot from Tucker until that is resolved, but I doubt that silence is due to any no-compete clause, IF they failed to show cause. If it's true that they are buying out his contract, that seems to be a big tell. Truth is none of us knows how his contract reads, so we're all speculating.
Bet everyone is chomping at the bit to be the first to interview him.