This argument may be valid in some jurisdictions but not all even in the US.
Here in New Zealand the taxi industry was deregulated some 20+ years ago. Requirements are an appropriate level of licence, police check and a vetting by the govt. Transport Authority that you have the right structures, log books etc.
No monopoly exists to any one firm in any major city but the pre- existing firms have maintained their dominance in the main: e.g. Auckland Co-op, Black & White Cabs (Wgtn). Why? Better service and fewer horror stories of ex and current rapists etc. driving cabs.
The regulation that exists is mainly for the protection of customers and being able to ensure the vehicles are safe, drivers work no more than the maximum number of hours and so on.
So, a light handed regulation mix and Uber will not comply as they are 'not a taxi business', the NZ Police are prosecuting them because they are.