You're describing a business model that (in theory) has a massive built-in cost advantage over Uber (whose model sounds bloated and inefficient compared to yours). The start-up costs are lower, the operating costs are lower, the maintenance and keep-up costs of a single Web site are lower.

Why hasn't anybody executed on that strategy (in practice)?

Forget the government affiliation, someone could be minting money either by competing with Uber on cost or just strategically choosing smaller markets that are not yet covered by Uber.

Why aren't they?