I think employers could have a company policy that you cannot have any kind of side-job, in case it influences your primary job. I used to have company rules that said I had to ask for permission for a second job or board job. They wanted to prevent me from doing something competitive.
But I understand that how lower salaries they pay, the less reasonable this becomes.
On one hand, I understand your point, kinda. But on the other hand:
1) You're dealing with humans, not machines: their lives WILL influence the job. What else are you gonna do? Forbid people from dating (drama influences their ability to do their job), getting married (wedding planning and distraction influences their ability to do their job), having kids (parental leave, exhaustion, etc: ALL likely to influence their primary job) divorcing (oh god the drama), having parents need elder care or passing away (how much time off work do you need to take care of your mother's Alzheimer's??) etc. Like, things people do outside the office influences their job. Period. It's 100% out of the employer's control, despite what some employers would like to think (and I say this as a manager, ok - if the people I manage have a sick kid and are going through a divorce, I have to adjust workload because they can't handle it all because their attention is split, and that's NORMAL for a period of time. It's life.)
2) I think that pre-emptive "we forbid this because it MAY influence your job" is straight-up rules-lawyering your way out of having to manage, and is shitty management. Like, if I, say, sell eggs from my chickens on the weekends, and go to the farmer's market on Saturday mornings to sell some stuff I made, hypothetically: based on what you wrote, my employer should be able to forbid that use of my free non-company time 'just in case' it influences the time/effort I spend at work - which, personally, I think is bullshit. I trade a portion of time for a portion of money, I do not trade ownership of my life for money. That's not the deal.
REGARDLESS of the contract I sign, though, if my chickens and baking (or whatever it is) infuences my ability to commit to and do my primary job, it's 100% reasonable and legal for my boss to have a conversation along the lines of "we have noticed that since you started doing this thing outside of work, you have been late 5 times, called in sick twice, and been absent-minded, which has caused the following mistakes to be made. We need you to commit to fixing this situation. Can you suggest some concrete steps you can take to ensure that these issues will not re-occur?" AKA: the problem is NOT the side-job, the problem is the impact on the ACTUAL job, and it's the manager's actual job to address that.
Oh, and 3) Look. I'm actually getting chickens in the spring: what I'll save on compost and groceries and meat, + the money I can bring in selling eggs and meat, after expenses, should equal to 2-300$/month, depeding on the season. Etsy brings in 50-100$/month, depending on what I feel like putting up there. The occasional freelance gig brings in a few hundred, when I have time around family and work and life. That's 300+$/month of my expenses that don't depend on my employer to be met, right? Saying 'no side gigs EVER' is functionally also saying 'we require you /possibly your family to be dependant on a single source of income, and this will put you in the worst bargaining position EVER, because we also know you can't afford to leave because you have no other source of income. Cheers!'. That's double-plus bullshit. I can understand why a (shitty) employer would find that appealing, but it's a super transparent power play and is nonsense.
In reality: most employers have a clause like this, and then turn a blind eye to anything that isn't direct competition. I just still think it's bullshit.