That's a reasonable argument, however, without strict legal restrictions that gets stretched as far as fast food employees being prohibited to go work at another restaurant, which is ridiculous on one hand and very understandable on the other - they have little bargaining power to refuse the clause, and a non-compete means they'll be less likely to leave so it allows the employer to keep wages low.

Using a non-compete for that is overreaching. You could simply ban that much more specific behaviour you're trying to prevent.

Yes, companies can have non-solicitation agreements which are IMO quite reasonable so long as they cover a reasonable time period and AFAIK are generally enforceable.