No, there are plenty of languages in primitive cultures that are highly
irregular. They're mostly cultures that civilized man has barely touched.

As I pointed out, what's the difference between "regular" and "irregular"
when there are so many rules that each particular one is only rarely used?
All an exception is, after all, is a rule that only works on a few words.
You can call them all rules (regular), or all exceptions (irregular), and it's
the same thing.