Why does the Uniform Vehicle Code take away a cyclist's right to use most of the roadway? Why does the Uniform Vehicle Code take away a cyclist's right to use most of the roadway, restricting him or her to the far right? 

Considering (1) the numerous exceptions to the 'keep far right' law, (2) how often a cyclist encounters these exceptions*, and (3) that every exception is safety-related, answers which suggest that keeping far to the right makes the cyclist safer must cite scientific research for support.



*Consider this example. The average car, bus, tractor trailer, and cyclist are 6, 8, 8.5, and 2.5 feet wide respectively. The minimum 'safe passing distance' is 3 feet (or more) wherever it's defined by law. Assume the cyclist rides 1 foot from the curb. (8.5 feet + 3 feet + 2.5 feet + 1 feet = 15 feet) Any road less than 15 feet wide is, by legal definition, substandard width. And since every travel lane in a cyclist's city or town is probably 12 feet wide or less, the cyclist may use the full lane virtually everywhere.



Note: Here are some relevant passages from the Uniform Vehicle Code (of the United States) for quick reference. I omitted some wording for brevity's sake. Visit the linked PDF if you wish to read the entire passages. 

"Every person... riding a bicycle shall have all of the rights and all of the duties applicable to the driver of any other vehicle under chapters 10 and 11, except as to special regulations in this article..." - Uniform Vehicle Code, 11-1202, pp. 168

"Any person operating a bicycle... shall ride as close as practicable to the right-hand curb or edge of the roadway except under any of the following situations: 
1. When overtaking and passing another bicycle or vehicle proceeding in the same direction. 
2. When preparing for a left turn at an intersection or into a private road or driveway. 
3. When reasonably necessary to avoid conditions' including but not limited 
to: fixed or moving objects; parked or moving vehicles; bicycles; pedestrians; animals; surface hazards; or substandard width lanes that make 
it unsafe to continue along the right-hand curb or edge. For purposes of this section, a "substandard width lane" is a lane that is too narrow for a 
bicycle and a motor vehicle to travel safely side by side within the lane. 
4. When riding in the right-turn-only lane." - Uniform Vehicle Code, 11-1205, pp. 168
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)