It seems to me Uber's management openly disregards their workers (but tell me if I'm wrong) and they openly disregard other social goods such as the law. I see this in actions and occasionally in words too.

If Uber becomes the dominant service, which due to the network effect would be the only place to find customers/drivers, what will they do to their workers?

There's no reason to think Uber will, out of the goodness of their hearts, do any less than use their full market power to take as much as possible from their workers.