I think we need more than an either/or. Not many employers in the US allow a person to set their own hours and locations.

Divorcing health insurance from employment entirely would help a great deal.

And where does the line go?

Can you please elaborate, because, in the case of Uber/Lyft, it's simple, if you force when drivers go, they can't refuse clients, etc. Then you are not "just" a platform to connect driver and people looking for a ride. If you are imposing rules, other than local regulations, to the drivers, you are an employer, and you should follow labour law.

If you use Stripe API for examples, if you follow the law, and their T&C of services, they can't force you to sell to some clients, etc.

So if you do only one of those things are you still an employer or now a platform?

I'm still confused, because you are not giving any example or explanation for "one of those things".

As soon as you tell somebody how to make their money, outside of government regulations, you are in fact an employer.

Which is different from a contractual work where you can define requirements. In the case of Uber/Lyft (and other Gig economy for that matter) you do not sign a contract with each transaction you do with them.

Therefore, your contract with them, it's to pick up and drive users of the platform under terms set by the platform. This is obviously an employer - employee relationship.