This is irrelevant. In reality, the Judaic tradition has always upheld the verbal tradition as legit, that's why there are variant views regarding some non-important things in the Jewish Bible. The mistake here is thinking that Jesus was upholding the traditions merely by disagreeing with the Pharisees. No, His message was different, but related to, the teachings in the Temple. Jesus taught a religious practice that didn't 'replace' the verbal tradition, merely shifted the emphasis from a more academic one, to a more spiritual one.
His emphasis did not include a rebuke to his own for not washing before eating, for being homeless essentially, water is not always easy to find, even grey water which is undrinkable...these kind of things were so unimportant that to wash the outside of the cup was considered moot, at least in time and place. Mikveh baptisms were not done often, but WHEN they were done, a cleansing or spiritual washing before God did take on very much new meaning. Since they were as dirty as people get who do not wash every day their whole body.
I agree that verbal tradition was considered valid, the THREAD of thought underlying metaphor, which may have slight variance. It was in fact essential to do this, find the underlying principles and THREADS of truth behind variant oral testimony, since certain words may be changed around, a jot here or a tittle there misplaced. That part of the halachic system was necessary, but not necessarily inspired as the original oral testimony from the mouthpiece of God. What Jesus meant by "no jot or tittle" will pass away without fulfillment, is the ORIGINAL testimony, which must necessarily be "oral copies" upon other "oral copies."
The secular/rational POV is indeed superceded by spiritual comprehension, and this by faith. But faith does start with common sense and this in survival mode, since we have to use this same mechanism...to survive unto life, whether temporal or eternal.