Why does the Uniform Vehicle Code take away a cyclist's right to use most of the roadway?
The short answer is:  the US "Uniform Vehicle Code" is not law and has no direct effect on road users, so the core premise of your question is misplaced. The UVC is a suggestion as to how legislators might choose to write laws, and also how judges might choose to interpret them. So it neither removes nor recognises rights, and your question could perhaps best be interpreted as "how much does the UVC influence lawmakers" which is unanswerable. So I'm going to address "how do road rules differ between cyclists and motorists", using the example of New Jersey since I prefer that question.

More generally in the USA as a whole, motorists have no right to use the road at all while cyclists do. Viz, a motorist can be forbidden to drive but a cyclist cannot directly be forbidden to ride (there are avenues like parole conditions, however).  So in that sense cyclists have many more rights than motorists do. However, a licensed motorist travelling in an approved motor vehicle has permission to do many things that cyclists are legally forbidden from. The road laws vary from state to state, and also within the United States of America.

You will find that the generic rule is that "all vehicles must travel as far to the right as practicable" and that cyclists actually have more of a list of common situations where courts have decided that "as far as practicable" does not exclude the implicit "without dying" that lawmakers thought was obvious. So there's a list, mostly as a response to case law. Cyclist fined for not riding straight ahead from the right turn lane... exception written into statute "cyclists may ride in the straight ahead lane when travelling straight ahead".

You are correct that in theory almost all lanes are "cyclist may use full lane", except that de facto law very rarely corresponds to de jure. Viz, most road users habitually break the law. So it becomes a judgement call on the part of the cyclist as to when it's a good idea to take the lane, and when not.

We are seeing some interesting developments with self-driving cars in this area as it has become obvious that if they always obey all the laws they won't be able to operate on public roads. One simple example is following distances on motorways/freeways. Since most motorists drive in the suicide zone all the time, a self-driving car that allows a safe braking distance behind the car ahead is also allowing enough space for a human driver to feel comfortable moving into that gap.

(edit to add)
An example of the "keep to the right" law:
Keeping to the Right (New Jersey)


  The laws of New Jersey require motorists to keep to the right, except
  when passing. Motorists must drive on the right half of the roadway
  unless driving on a one-way street. Motorists must drive a vehicle as
  close as possible to the righthand edge or curb of the roadway, except
  when overtaking and passing another vehicle. (N.J.S.A. 39:4-82)