Irregular verbs Thank you Ludwig for your answer.
The consequence is that what are rules for language learners are habits for first-language speakers, and that use and practice determine what the rules are. (The same applies, nowadays, to dictionaries, as I'm sure you are aware.) — Ludwig V
I agree in this point. You even have read my mind because I was about to post some lines related to how these rules work when you are not a not a native speaker but a learner.
When I learned English in both school and college, my teachers never explained to me why regular verbs with "-ed" and irregular have exceptions. Yet, when I failed more than one English grammar text, those teachers simply said: "please study harder the English grammar"
But according to Steven Pinker, it is not something to be ashamed of. I didn't have the rules in my mind, so I simply put "-ed" in the verbs, whose irregular form I hadn't learned yet.
Grammatical irregularities (which don't occur only in verbs) are a serious nuisance to learners. Sadly, use and practice pay little attention to their problems — Ludwig V
All children (and myself included) make error in the speech like this: "My teacher holded the baby rabbits and we patted them"
Berko Gleason analyzed this pattern in an experiment with 4 and 7 years old kids.
Gleason stated that children are not parrots who just play back what they hear. Children therefore are not like pigeons in a Skinner box, who increase or decrease the frequency of responses in reaction to contingencies of reinforcement.
You mentioned Chomsky and yes, he and Eric Lenneberg are pioneers in this field and they both stated that children's ability to generalize constructions such as the regular past tense is actively acquired by a special rule-forming mechanism in the mind of the child.
All languages force to their speakers to memorize thousands of arbitrary words. Languages differ in their division of labor between simple words and grammatical combinations, and some, such as Native American languages, have fewer words and more rules. But even in these languages speakers cannot deduce the meaning of most words from their sound, and must commit whole words to memory.