Of course there's not one on-duty staffer per car. You'd only need that many people if all rides required human support at exactly the same time. But in reality, most rides wouldn't require it at all. Even if there's likely to be some correlation between support requests, it'd be all cars on one street or block needing help at the same time, not all cars in the same city.
> Also, is there any path to profitability given how many billions were poured into the technology?
Sure, let's do it back of the envelope.
First, the unit economies. Let's assume that a taxi is driven for 16 hours per day (two 8 hour shifts), and the average wage for a driver is $15 / hour. That works out to 16 hours / day * $15 / hour * 365 days/year = $87600/year. This is how much less it costs to operate a self-driving car is than one driven by a human. Since human-operated taxis won't be running at a loss, this means a self-driving taxi would make a minimum of ~$90k/year profit if it got as many drives as a human.
Would they get as many drives? Would people prefer a self-driving taxi over a human-driven one? At least if the self-driving taxi is cheaper, I don't see why not. It'd be easy for the self-driving taxis to undercut human drivers on price, while still remaining very profitable. The big challenge is the service area, where self-driving cars currently have no flexibility.
The unit economies seem to check out. Is the market big enough to run this as a proper business, or is it depending on unrealistic growth? The numbers I'm finding aren't super consistent, but it seems that the taxi + ride-sharing business is something like $50B-$100B / year just in the US. The addressable market is definitely sufficiently large to pay for billions in R&D.
So really it's just a question of how fast they can scale it up, and how quickly the competition catches up.