We sometimes need to main insertion order because we need the insertion order to solve the problem at hand. Sounds a bit tautological, but that's really pretty much the reason. Some data is ordered but also benefits from random access.
Likewise for sorting. It gives a way to find the "next" or "previous" item very cheaply, while still being reasonably efficient for arbitrary lookup. One example are approximate lookups, say, you know the entry you're looking for starts with Foo
but you don't know what the rest of the key is.
Hashmap exists to make things faster and simpler (no concept of order) when you don't need any of these operations, only exact lookup.