No, it won't.
> The fundamental economics don't change...
They don't change for Uber, but they do for drivers.
> It will take longer to get to penetration levels that result in sufficiently high utilization.
You seem to be under the belief that supply drives demand here. That's not the case.
The economics of utilizing a taxi service can be markedly different for suburban consumers than urban consumers. Point B is frequently more distant from Point A in suburbia, so the average cost of a taxi ride tends to be higher. Thus the relative attractiveness of paying for a taxi ride decreases.
Perhaps it doesn't work "as well", but I live in a very-much suburban area that borders on rural. I know several farms from which where one can consistently get an UberX with a 5-10 minute wait.
For example, the further you travel, the more important cost per mile becomes in deciding car vs. Uber. As with every other own vs. rent discussion, the more you use something, the more compelling ownership is.
1. People will move back to cities as cities become more attractive (thanks in part to things like the shared economy). There's already some evidence of this trend among millennials. Reverse white-flight if you will.
2. Uber will eventually work just as well in suburban areas. The fundamental economics don't change (higher resource utilization => lower costs). It will take longer to get to penetration levels that result in sufficiently high utilization. But we'll eventually get there.