The cost of that $7 are the billions they lose every quarter. It's not sustainable. They're a public company now, so to come up with fresh cash, they have to issue bonds and pay interest on them. How will they repay it when they aren't generating fresh cash through profits? They can't rely on VCs opening their wallets whenever they needed money.
They will raise prices eventually, they are in the "get a lot of regular users" phase still, growing that until they are ubiquitous.
Yes, they may face monopoly concerns then, but that is down the road.
What they will not face is competition from the $30 taxi companies, because unlike the taxi company they do not own any cars and the resultant costs of that.
Cheap rides are to gain marketshare and customer acquisition. Not saying the strategy will be fruitful but it is a strategy.
I use Uber all the time, as does everyone I know. Hell, I even drove for them for a while.
They provide a needed service and they are subsidizing that to get rid of competition like Lyft and to grow a huge user base. Then, it's likely they will raise prices and start making money.
But it is not a Ponzi scheme. Last I checked, a local taxi company that is still in business wants $30 to take me into town, which is 5 miles away. Uber is $7.