It is difficult to predict real-world distortion from idealized triode or pentode models. The models assume tubes with perfect physical assembly and ideal emission characteristics. In practice, grid windings are not evenly spaced, grids are tilted a little bit, coatings on the cathode are not perfectly uniform, and there is always just a bit of residual contamination. Tubes are not built by robots, but skilled technicians, and as a result, they are all a little different from each other. By looking at spectral distortion measurements, patterns that are unique to each manufacturer emerge, and none conform exactly to the tube model. (The map is not the territory.)
Successive stages multiply distortion terms as more and more kinks end up in the transfer curve. Of course, this applies to the entire transmission chain from microphone to loudspeaker, with everything in-between.
Models are useful for finding bias points and the expected high-frequency response, but predictions of high-order distortion can be way off from the tubes you can actually buy. Low-order terms like 2nd and 3rd harmonic distortion may conform to the model, but I wouldn’t trust it further than that, not with real tubes. Think of the models as first-order approximations.