Verb irregularity is often overstated as a complexity in English. For example, my French-English gives 120-ish different classes of verb conjugation, but most people would say that it has ~4-ish classes, plus some simple modifications on top of that, plus random exceptions here and there. If you tried to group English verbs into similar conjugation classes, you'd arrive at probably a smaller number. It's just that, because English has so little conjugation left, it's easier to list out all of the exceptions as a single list.
English's problems generally stem from the Great Vowel Shift destroying our spelling (and ruining the remnants of the Germanic ablaut system for conjugation), and, most importantly, our proclivity for borrowing foreign words with foreign spellings and foreign conjugations. Doubly so when we can't even conjugate the foreign words properly (it's supposed to be octopodes by that rule, not octopi; octopuses is perfectly functional reasonable).
English's problems generally stem from the Great Vowel Shift destroying our spelling (and ruining the remnants of the Germanic ablaut system for conjugation), and, most importantly, our proclivity for borrowing foreign words with foreign spellings and foreign conjugations. Doubly so when we can't even conjugate the foreign words properly (it's supposed to be octopodes by that rule, not octopi; octopuses is perfectly functional reasonable).