One advantage to randomization, and why various languages did it in the first place, is that it prevents miscreants from DoSing your service if they know its implementation.
Say you're operating a service and you share its source on GitHub such that anyone can see it. Your language doesn't randomize hash values. Hashes are O(1), right? Well, not if a clever attacker can send you a set of values where they know each one will hash into the same bucket. The you end up with like 9 empty buckets and 1 with 100,000 items in it. Oops!
Old Python pre-randomization had a dict.items() method that would yield all the keys in order, conceptually kind of like:
for bucket in self._buckets:
for item in bucket:
yield item
The order of those buckets would be repeatable between runs, so bucket foo would always come first, then bucket bar. Then Python added hash randomization so that the resulting hash key was something like hash(salt+key) instead of just hash(key). Now there's no way to tell in advance which bucket an item would get filed into, and the buckets would end up more or less balanced in size.
Newer Pythons (since 3.6? 3.7?) do something altogether different, and I can't explain exactly how their ordered dicts work, except to say I sat through a presentation on them and thought it was freaking genius even if I could re-implement it myself without sitting down with their docs.