I am not sure if a web-client would do the job. From my knowledge, interacting with maps on a mobile browser can be an aggravating experience. If an app doesn't do the job, isn't immediately useful, people discard it without further consideration which makes B2C things tenfold hard.
The surest way I see for it to work is to start as boring-taxi company that has a phone number and a person at the end. Then, slowly move into automated app-like way. I am guessing that's how OlaCabs, India's Uber, got started. Automation is awesome but there are so many points of failure in Uber-like venture that it's better to be safe by doing manual tasks.
I've thought about a virtual secretary but I'm not so sure how helpful it would be. They would need pretty specialized knowledge to be able to help much with support requests. I don't have so many meetings that I can't schedule my own.
As far as Uber for your country. Does Uber not exist where you are yet? There was another one in Malaysia called GoTaxi or GrabTaxi that I thought was interesting. It connected you with 'real' taxi drivers for a pre-arranged flat fee for the ride. One guy told me he used it just so he had a record of what taxi he was in incase he got robbed by the driver.
Edit: latent thoughts
That sounds interesting actually. One of my biggest concerns is push back from the local taxi union, so that may be a better way to approach it. I'll definitely look that service up.
I have a couple of ideas I've been wanting to work on, but time is quite scarce as a grad student. I guess it's partly because I tend to overthink (and over-design) my ideas, and end up getting overwhelmed before even touching a line of code! What's even worse is that the majority of my ideas are intended for my home country (EST+6 timezone), since I think it's much harder to be successful in an over-saturated market like the US.
For example, one of my ideas is designing an Uber-like service for my home country. The current roadmap (which I haven't started on) is as follows:
1. Design a basic placeholder site with some info on the app/service
2. Run a limited ad campaign to gauge interest and ideally collect emails (Google, FB, local radio, local newspapers)
3. Try to get interested users to fill out a survey
4. If the results from 2) and 3) are promising, start developing a barebones MVP
5. The MVP will target one city, require manual signup for drivers, and only have a simple web client
6. If successful, start hiring local developers, optimizing server-side, and designing an Android app (iOS is a very small market)
Any advice for someone in my position? I'm open to all types of feedback from any HNer - it's always good to get an opinion before working on something like this!