(edit) The article suggest self driving cars, and by extension Google's ridesharing service won't be ready for 2-5 more years.
And Uber's customer-base is price sensitive. You can easily get into this market if you're willing to price compete with Uber.
Now, Uber is very willing to price-compete ferociously. It will absolutely drive you both deep into unprofitability. And Uber has quite a war-chest, and it can push around its smaller competitors this way. But as rich as Uber is, there are plenty of companies that are richer. Way richer. Orders of magnitude richer.
I think that so far, the really big boys have said, "Why do we want to get into a price war with Uber? They'll fight until the last breath, I don't see why we should launch a deeply unprofitable ride-sharing service."
Amazon might do it eventually. They have expertise in operating at high scale, low-margin, and they're big enough to destroy Uber. They also might want to use a ride-sharing service to deliver goods. I think that right now, they've mostly said, "We're unconvinced that there's a real logistics business here, and so we aren't going to get involved."
Google might do it for the data.
I can't see Apple bothering -- it's pretty far outside of their corporate comfort zone. But if, I don't know, Tim Cook gets hit by a bus and their new CEO wants to make major changes, they absolutely COULD do it.
Microsoft could maybe do it in an attempt to create a compelling entry-point to their ecosystem, but it's not very Microsofty.
I don't see that any non-computer companies currently have a reason to try it.
That's why Google has an advantage over everyone else - for them it's a one-sided marketplace, they don't need to worry about the driver. And that gives them a big cost advantage over Uber.
Neither Uber's passengers nor their drivers are deeply loyal. They are for the most part brought to the service by the value prop. Uber is of course an established brand, and that brand has some value, but the value is hardly infinite. A deep pocketed competitor could establish themselves.
This sort of cross-subsidy has a poor track record when used against well-capitalized opponents. (In many situations, it's also illegal: see "dumping".) Unless you can complete wipe out the competition and force them out of business, you're pouring money down the drain, and building nothing of value with it. Bing Cashback resulted in most people doing their searching on Google, identifying what they wanted to buy, and then buying it on Bing so that Microsoft would pay them.
You get very odd arbitrage situations that basically result in funneling money straight from the corporation that's being idiotic to a savvy consumer. If a company did what you suggest, I would immediately sign up with them, along with my fiancee. We would then use the app every time we took a trip together or picked each other up. Since one of us is the driver and one is the passenger and the driver earns more than the passenger pays, we'd be making money at this company's expense every time we drove somewhere. Now imagine every carpool, group of friends, or just random strangers who setup a business to exploit this arbitrage opportunity doing that.
And, just to be clear, that's what Uber does. Not in as simple and straightforward a way as you're suggesting, but at least large fractions of the time, it pays its drivers more than its passengers pay it (for example: it's constantly giving me $10 coupons. It has sign-up bonuses and income guarantees for drivers. Etc.) Of course, it's spending investment money, not money from its other non-existent businesses.
So if you and your fiancee want to try this business, you can do it right now with Uber. Or Lyft. I suspect you will find that despite the fact that there is theoretically a fair amount of money on the table here, they've made it obnoxious enough to get that you won't bother with it.