Not joking btw. It's rather amazing that employers who expect rational, logical decision making on the job want applicants to suspend their reasoning and good judgment when it comes to negotiating compensation and employment terms.
Which is when you move on to the next employer if at all possible.
A court will be much more favorable to the applicant, then, because presenting them with a contract they have little power over is something courts generally don't like, as it is unjust.
Asking the employer to write "this is a contract of adhesion" basically means "oh, you're screwing me over? Can you please write that this is a screwing-over contract on it?".
Courts uphold shrink wrap and click-to-agree contracts all the time.
(ETA:) This might not help very much, because in places where noncompetes are standard, a court would be sticking its neck out a little to rule that one is unreasonable. But maybe it would help a little, if one couldn't get the provision struck from the contract altogether, and had no reasonable alternative to accepting the job. (Again: IANAL, and I'm just speculating -- no one should take this as legal advice!)
I wonder what would happen if you said "Ah, so you're stipulating that it's a contract of adhesion. I'd like that in writing, please."
Contracts of adhesion can be harder to enforce [0].
(IANAL, and I'm not necessarily recommending doing this, but I am curious what kind of response one would be likely to get.)
[0] https://en.wikipedia.org/wiki/Standard_form_contract#Contrac...