A fully independent contractor like a SuperShuttle driver can treat each fare as a separate contract, pick only the best offers, and generally not provide the company an adequate service level to ensure a reliable stream of customers. Each driver prioritizing their short-term interests keeps that model from being a viable profession in many cases.

On the other hand, an employer is required to provide certain benefits to employees, especially if they exceed certain thresholds of hours worked. To make the fixed cost of some of those benefits viable, the employer will usually want to require the employee to work specific hours, and often limits those hours to stay within legal thresholds.

It's the flexibility of scheduling I that I think attracts people to gig work. They'll take the ability to cherry-pick the most profitable gigs if given the chance, but it isn't a core requirement.

It's probably desirable to add a third category to provide gig workers some protections without shoehorning them into the employee classification, which many of them actively wish to avoid.

Such a simple concept yet many ignore it. Nowadays it's trendy to call such concepts "mental models".