Some of this 'uncertainty' sounds somewhat... exaggerated. I've worked on fluid and stress models for heavy earth moving equipment (not the engineering side, but the technical simulation side... I'm not an engineer) quite a while ago (12 years or so) that was incredibly detailed and had little if any variance to real-world testing. Air flow over surfaces including turbulence models gets into incredibly dense math, true, but it's fairly well predictable as long as the model is correct.
Sure, there could be some fundamental errors in the CFD models that result in the FH shredding itself at MaxQ or something similar, but I wouldn't put it at 50/50.
So, none of this matters for why rockets are so hard to make. The real reason is quite simply: design tolerances. The most devastating kinds of stresses on a rocket are coincident bending and shear, and those are quite hard to 'solve' even for large transients without expending a lot of material on the envelope. All material at launch has growth factors of 100+, so you really want to minimize material use wherever possible, especially on the first stage.
Most of the peak loading on rockets is not analytic at all. It's stuff like acoustic loading during launch (due to the ground effect) and during max Q when shock formation propagates and often resonates in the structure. These are loads that can constructively or destructively interfere with each other. Combine that with the inherent stochastic nature of the frequencies of sound waves you'll get and it becomes really treacherous to 'properly' design for the maximum loading you can expect. The maximum loading can be some resonant mode that happens once every 100 launches, and that particular loading can suddenly increase stresses on some subsection of your vehicle twofold.
So you do eigenmode simulations, you thoroughly diffuse the most critical shock front formation sites, you modify the speed of sound through your structure to avoid significant acoustic energy transmission and so on. But that only goes so far. The tools we have nowadays are really not that much different from the Patran/Nastran days of the 90s, just an order of magnitude or two faster. CAD software can't just 'model a rocket'. You have some abstraction of your rocket as a rasterized model, you enter some boundary conditions and constraints and then... you let it run. Some engineer needs to adequately design the model, the loading and the boundary conditions to adequately simulate what goes on. Often, this is done on e.g. a few-degrees section of the symmetrical rocket and just assumed to generalize to the whole structure. Not because that is the best practice, but because simulations still aren't fast enough to simulate on nyquist-satisfying grid spacings.
The rest of the aerospace industry has it easy. Airplane manufacturers just design their absolute maximum loadings at 2x or 3x of 'normal' flight conditions, because airplanes can be way too heavy and still economical (and any crash will cost them orders). Rockets don't have this luxury, so... they blow up. A lot. Fact of life.