Why should one model an entropy source in order to build a TRNG? Some  assert that a theoretical model of the unconditioned source must be created when building any TRNG. It's believed to be a fundamental requirement.  So a few related questions arise:-


What is a "model"? For example, are we talking a simple histogram of the raw output distribution, or something like $ \sigma^2_{quantum} = \frac{\gamma}{\gamma + 1} \langle V(t)^2 \rangle $ thus $ \sim H_{Shannon}  $ in laser phase interference? 
More generally, do they mean   a posteriori (empirical summary statistics, probability density function, $V_{RMS}$ , $\delta^2_{signal}$)  , or a priori (predictive) modelling like the $ V \sim -C_1(1 - e^{-\frac{t - t_a}{C_2}})  $ capacitive charge curve that governs the shape of Zener diode breakdown and the earlier laser equation? The major difference being that an empirical/a posteriori model is agnostic to any physics. Yet underlying physical processes are often mentioned.  
Is there any original theoretical work justifying this modelling requirement? I'm asking about any works underpinning or justifying what one might read in a NIST/BSI AIS document.
What to do if the empirically measured entropy rate does not agree with a priori (predictive) modelling? Say a very significant error. A measured noise signal can easily increase 100% between two generic component types from different manufacturers (eg. BZX85C24 Zener diode).


Update:

There is now a hot network question - Is a model fitted to data or is data fitted to a model?
 Currently answers are leaning towards the empirical data taking priority over the theory. So you'd start with the oscilloscope and work upstream to the physicsing[sic]. As a philosophical empiricist, this seems more intuitive to me but there does seem to be a portion of members here that give precedence to   math over  measurement. It's a Plato v Aristotle question and I'm trying to be  open minded on this one.
Why use a model?
The utility of a scientific model is the ability to make predictions. An example of a simple model is one describing the motion of projectiles based on Newton's laws of motion and gravity.
You could use two strategies on a battlefield to make a cannonball land where you want it to.
You could point the cannon in the general direction of a castle and fire. If the projectile flies over the target you try again, aiming lower. If it still overshoots the castle you aim a little lower again. (Or if it falls short aim a little higher.) You try and make adjustments until you get the result you want.
Alternatively you could determine the distance between you and the target, how much higher the target is than the cannon, the initial speed of the cannonball. You model the cannonball as a point mass. You ignore the effect of drag. (It might be fine depending on how dense the cannonball is, how thin the atmosphere, how far it needs to travel.) In such an environment, a consequence of Newton's laws is that the relative position of a projectile can be determined from its initial velocity. You use the numbers and formulas to determine where to aim. Not your eyes.
The first method does not use a formal model. It is not preferable because it will waste resources and because any mistakes will put you in danger. The second method (potentially) enables you to hit your target on the first try.
Science is full of models. You want to find one that is sufficiently accurate in order to have confidence that things will work out right. You want a simple enough model for it to be practical. The Newtonian cannonball model does not describe exactly how the real world works. It simplifies things while remaining useful. For some applications you need something more complex. All models are like that.

Example
If you want to build an RNG that uses radioactive decay as it's source of unpredictability, then first you model the process of decay using the half life model. It lets you treat the physical phenomenon as a clean mathematical abstraction.
Next we figure out how much of the material you have and what fraction of the decay events we can detect. Then we use our knowledge that the half life decay model can be described as a Poisson process to create a statistical model.
The model will tell use how likely we are to detect an event in any given time slice of a certain length. If the half life is long enough and we have enough material this probability should remain accurate for a long time.
Now we have a Bernoulli process. The samples are binary (detection or non-detection), independent, and will have effectively constant probabilities.
We can look at the probabilities of the two possible outcomes. From that we can easily determine the min entropy. That number can tell us how many samples we need to take to ensure we have sufficient entropy. (And therefore also a lower limit on how long we need to wait to generate a key.)
Multiply the number of samples you need by 2 or 2000 just be conservative and paranoid. Now you know how many samples to process through a cryptographic hash before you can use the output to generate a key.
We could have stopped once we knew we could model detection as a Poisson process and not calculate probabilities. Two non-overlapping time slices are statistically independent in a Poisson process model. We could use von-Neumann's debiasing algorithm for that reason without needing to know the detection probability because (assuming the hardware is working correctly) the kind of samples we have are independent and identically distributed.
But calculating the probability gives us the opportunity to test if things are working as intended. (Use a better model to build a safer HWRNG.) If the CPU sees detections far more frequently than expected, then maybe someone is using another radioactive source to try to bias our RNG. If we see too few detections or too many identical consecutive samples then maybe a circuit has been damaged.
Note: I'm confident that I don't know how every real world radioactivity-based HWRNGs work with 100% accuracy. There could be different designs with different design justifications. Physics is not something I plan on studying further. And I'm definitely not going to bother with reverse engineering proprietary things.

Other questions
Use a histogram?
No. Don't use a histogram. Use a probability mass function.
Creating a histogram requires sampling. A histogram can only be used to estimate probabilities. If you don't know what to look for then you definitely can't tell the difference between a working system and a broken one.
You also don't want to calibrate the system based only on empirical results. It's important to know how likely components are to fail, to know whether or not aging of components will render the calibration invalid.
Calibrating to lab conditions is dangerous because the characteristics of the entropy source you use might be different at different temperatures, in different environments, as the components age, when exposed to different strengths and frequencies of electromagnetic noise, on different power supplies.
It's a better idea to use a design based on knowledge of a physical process that will be robust enough to still be unpredictable (and predictably unpredictable) in the future under different conditions.
Theoretical necessity?
Theories for why you don't need theories? Maybe. I don't know how many theoretical researchers have an interest in that niche.
Results don't match theory?
You're model is wrong or your hardware is broken. If a device isn't working the way it's expected to and there are any safety implications if it's broken, then why not fix it or use a different device? If your model is wrong and your hardware is fine, then why not find a model that does explain things?
50% error?
I don't know what metric you're using. That sounds really high.