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The other possibility is that they are irregular because they are very commonly used and thus are invariably learned very early by every speaker, and used so often by all interlocutors of all early speakers that there is little room for misinterpretation: everyone converges on the same behaviour. The root of all language change is innovations, often rooted in misinterpretations, by language learners, and (with a few exceptions such as present-day English and various creoles and trade tongues) that mostly means young children. Parts of language that are highly used around children will tend to smooth away the childrens' errors (many of which are regularizations of irregular forms: oh look pronouns are highly irregular).

For an example, look at English pronouns. They're inflected, they're fairly bizarre in all sorts of ways, and they are almost unchangeable. People have been trying to introduce a third-person gender-neutral pronoun less contorted than singular they for centuries. It has never caught on, and it likely never will, because pronouns are nearly universal among the community of English speakers, so there is little dialectical diversity to exploit in generating new pronouns, and all early speakers learn the same things (and, at the least, correctly learn their dialect's variation).