Is there a physical reason why phase should be uniformly distributed?
A zero mean complex white noise process has a uniform phase distribution.  The uniform phase distribution would occur for any complex noise process whose I and Q (real and imaginary) components are zero-mean, independent and identically distributed.
The thermal noise floor common to radio receivers for receiving signals without other specific interference is typically well approximated by a zero-mean complex white noise Gaussian distribution; meaning a white noise Gaussian distribution on I (the real component) and Q (the imaginary component) and these two are independent from each other. This makes sense if you consider that the real and imaginary values for any given sample have no relation to each other and are also therefore independent. Within this restriction of having an independent and identically distributed random process for I and Q, the actual phase of any sample is equally likely as any other phase and is therefore uniformly distributed (regardless if the system is white noise or band-limited).
Complex quantization noise (using two real A/D converters in practice; one for the I channel and the other for the Q channel) will also be well approximated by a white noise process where in this case the phase is uniformly distributed as above but unlike the thermal noise example given above where the signed amplitude was approximated as Gaussian distributed, the amplitude for quantization noise is also uniformly distributed over a quantization level.