There is a philosophical discussion to be had about whether 19 physical parameters is "a lot", and another discussion about fine tuning. However, I was primarily referring to the artifical parameters that arise from doing real calculations (renormalisation scale, mass factorisation scale, PDFs etc). These plague pretty much all perturbative QCD calculations, and then particle physicists play games like varying them by a factor of 1/2 and 2 to get something that looks like error bars...
The number of SM parameters is not a lot, given the reach of the model, which is literally every physical phenomenon ever observed on Earth with enough detail, but gravity. Thousands of independent experiments, and observational data on a scale so absurdly large it's hard to state plainly. Any philosopher who wants to claim nineteen parameters is large is out of their minds!
Fine tuning, I agree, is a philosophical issue. I'm a physicist, and I don't buy it. Why does everything have to be perturbatively pleasant? Nobody promised us that.
The issue of artificial parameters is a red herring, I think. Properly computed, of course, well-defined observables are renormalization scale independent. You might have to pick a scheme/scale to do the calculation, but whatever scale dependence remains is an indication of some perturbative truncation. The continuum limit of LQCD, for example, produces real observables with no renormalization scale dependence. Hell, renormalization is not even mysterious in a computational approach.
