"If the worker is not integrated into the institution's operations and the right of control is not obviously apparent (no training, no work hours, no reports), you are reasonably safe as long as the relationship is short-term and the independent contractor has other customers."
I would say "integrated into the institution's operations" is the very definition of Uber drivers. (What is Uber except for a network of drivers?) And as far as "right of control": here's an app that tells you exactly where to go, who to pick up, what route to follow, how much to collect. Many drivers are not "short-term" nor have other "customers."
Drivers as a group are integrated into Uber's operations, but an individual driver is not. Nothing at Uber depends on a certain driver being available. Contrast that with most non-contracting jobs where operations depend on an employee being at work and doing their job.
Obviously there is no right of control of Uber drivers. They can choose to accept a contract or not, with no repercussions if they choose not to accept. The fact that the contract has clearly defined terms such as who to pick up, where to go, etc. does not mean the driver isn't contracting (since doing a job that has clear terms is the definition of contracting...).
Other than the 'short-term' aspect, Uber drivers are pretty clearly contractors by that definition.
They may be essential for Uber's business but that is different. Customers are also essential. Contractors can be essential.
First, despite all the discussions of Uber's/Lyft's full-time drivers, there are some proportion of drivers who are just people looking to make an extra buck on their ride home from the airport and whatnot. These drivers really don't expect/require a lot of money, and are just padding their income driving somewhere they were already going. I had a friend with a six-figure income who would do Uber rides in San Diego just because it was an easy way to cover gas occasionally. This is important because it changes the market for taxi drivers - suddenly a regular and lucrative set of rides (to and from airports) have clientele who expect much cheaper rides - even if the cost those clients expect to pay can't support an individual working full time at that rate. But even if full-time drivers attempt to avoid the platform, the market has substantially changed - they can no longer get the same price for their rides. Now, this may just be a market correction, but let's look at the second factor...
Uber and Lyft and burning VC money to power their operation - Uber lost ~$1.1 billion dollars in Q1 2019 , and Lyft lost ~$1.14 billion in Q1 2019 . These sorts of numbers tell us that Uber and Lyft are generating demand for an artificially low price for a service, which all but guarantees that the market for sustainably-priced taxi rides will be destroyed. Why would a customer purchase a ~$20 taxi fee when a VC-subsidised ~$10 ride exists?
The contention that Taxi drivers can "just not use Uber/Lyft" is pitting the depth of the pockets of taxi drivers against the pockets of Uber/Lyft's backers - it's not a reasonable expectation that taxi drivers can afford to wait out venture-capital subsidizing an unsustainable business model which destroys their livelihood in the meantime. According to the Federal Reserve in 2016, 46% of Americans reported that they would be unable to cover a $400 expense if some emergency came up . I don't think we can look at Uber and say "Taxi drivers could choose not to use it" - it's looking at the choice to use the platform in absence of the context of venture capital and the support which exists for low-skilled workers against predatory employment practices.
On the employee side: a driver can not delegate work, is paid per activity, takes no commercial risk, has no control over how they do their work and are not operating independently. On the contractor side: The driver supplies most of the equipment (that's if you don't count the massive server side investment as equipment).
So far tax purposes at least uber drivers are employees, so the question is why did the ATO give them an ABN in the first place?