Since Uber drivers are using their own equipment (cars), that also means they are not employees.
This is not true. There are plenty of professions where employees bring some or all of their own equipment.
One colleague of mine did end up using his own server to run daily data processing and numbers crunching jobs for work though. It also served the internal analytics web UI. Apparently went on for years.
I was definitely an "employee", if anyone is.
Crucially, this meant that I had to work the hours specified by my boss and make whatever deliveries he specified during that time period, else risk being fired.
In my opinion this was a very sensible arrangement. It was a good job and paid my college tuition. And pizza demand varies widely from time to time. It would be silly for the company to maintain a fleet of cars large enough for peak demand and then leave them in storage most of the time.
I've also worked as a software engineer, on salary, with a contract forbidding concurrent employment elsewhere, but done all the work on my own computer.
In light of the above, I don't think ownership of equipment is necessarily a meaningful consideration.