You'll definitely start finding more interesting and advanced melee weapons later, though only a very limited number deal non-melee typed damage--just some special cases.
Part of the reason is that (contrary to what you may see in some fantasy games, for example) a single weapon may only deal one type of damage. It would be a bit confusing if a greater number of melee weapons (or any weapons in general) did damage that didn't match their type. Weapon type is supposed to be a relatively straightforward indicator of damage.
That said, there are plans for more special items in the future, items that don't follow the normal design guidelines, so we could see some more special non-melee damage melee weapons in the future.
(Really though, you should get further in the world before making too many suggestions, because you'll find there is already a ton of different features to find out there, with variety increasing greatly the further out you reach!)