I want to revive this thread with a slightly similar question: does it make any sense to have more than one type of physical damage (blunt, pierce, slash), from a practical POV?
Having been in tabletop roleplaying a lot, the 'physical' damage type breakdown I'm used to is;
Blunt/Crush, Cut/Slash, Impale/Stab, Piercing/Bullet (combination of speed and size substantially change some things from 'blunt'), with some systems adding in Hacking/Chopping (swords cut, axes hack down trees). In video games I generally combine Impale and Piercing only because my brain sees them as synonyms and have hacking as an 'extreme' slashing type, if I use them at all.
As for a mechanical POV, they have zero difference from the more 'conceptual' elements. An element is just a name and special effects. You could rename every element in your game with a number and nothing would change except of course how much sense things would make to the player. You could have your elements be vehicle types, planets, the setting's pantheon, named after your cats, etc.
Now, if the question is "is it practical to have every weapon (or weapon type) have a given element?" then that depends on how you want to use elements in your game. Some games like everything having an element and then having ways to interact with those elements, with sometimes having exactly one nonelemental attack as a crazy way to get around the system. In one elemental system I had, 'metal' and 'wood' fell under the more conceptual elements and thus weapons were commonly one element and things definitely resisted or were weak to it. Other games want to 'restrict' elemental stuff to 'magic'. And other games want the opposite, forcing you to deal with weapon types while magic is just magic (or 'magic' is itself a singular weapon element, thanks Fire Emblem Fates!). Some games might even want 'physical' damage types for skills but not normal attacks (a sword just hits, but that Hidden Dagger skill the assassin has always crits and does slashing).
But at the core, it is the same question as 'should water and ice be different?'
One day we'll get a pokemon-style elemental juggling game based around the periodic table and no one will like it XD