Not free: okay, sure. But the barriers aren't that high. Let's take a look at the capital expenses: setting up some re-targeted advertisements isn't very expensive at all, and giving away a thousand rides at an average ride-cost of, let's say, $25, is only a $25k expenditure.
To recruit drivers (maybe in more than one city) might be a little expensive, just in terms of a time cost. If you're paying recruiters, that might cost a month or two of salary for every city you're launching in. Alternatively, some of these employees might just take an equity share in your startup.
The last big part is the design of an app: this could take a handful of competent engineers perhaps one or two months. This might be your biggest expenditure (a team of 10 might cost you $100k/month), but it might also be possible to pay them (partially) with equity.
I would wager that you could start up a competitor regionally (or perhaps even in a small number of cities) for less than $1M, which is a modest amount in the current tech. climate (specifically w/r/t/ venture capital). Especially considering the potential returns, it seems likely that some entrepreneurs will go for this.
And concerning regional competitors: yes, certainly. And it only takes a couple of competitors in every major city to make it very difficult for Uber to hold on to a monopoly or majority market share... :-)