I voted "No", because the question is whether there should be *extensive* weapon lists, and I dislike long weapon lists that include multiple items that are basically the same thing from different cultures or historical eras (like saber vs scimitar, or gladius vs short sword). Maybe a slight expansion, but not much.
My real wish regarding the weapon list is two-fold:
1. I just wish they'd done a little research and gotten the weapon names to match the historical naming conventions a bit better. I admit this isn't harmful to gameplay for people that don't know any better, but it bothers me. The historical longsword was exclusively two-handed, for instance, so that's D&D's Greatsword. Which means there's nothing on the list that matches the Viking/Arming sword (one-handed only) or the bigger Zweihander/Claymore types.
The sword list could be simple like:
Short
Arming
Bastard
Long
Two-Handed
Then add a few specialty items:
Falchion / Cutlass
Saber / Scimitar
Rapier
I don't know if eight sword choices is too few or too many for you, but I think it's the right balance. You could include cultural equivalents, like pointing out that the katana is just a single-edge bastard sword. That not be perfectly true, but it's the level of detail I'd look for in a game.
2. Without necessarily blowing up the list of items, make more meaningful and tactical choices between weapons available. Give players a reason to carry a few different weapons, and pick them tactically. Like axes are better versus armored opponents, and spears are good versus large beasts. Rapiers are useless versus armor. Etc.
I'd probably model the weapon vs. armor issues with Advantage/Disadvantage. e.g., Rapiers have Disadvantage vs Medium and Heavy armor.
Rather than go back to AD&D's "damage dice vs large creatures" rules, I might specify which size creature a weapon is designed to fight and provide the general rules "Creatures have Resistance to weapons one size smaller, Immunity to two or more sizes smaller." Swords and axes are for Medium opponents, Spears or pikes would be for size Large, and lances could hurt size Huge. You'd need special "dragon lances" to hurt something Gargantuan.
Make reach matter. A guy with a dagger really shouldn't be able to hit someone holding a sword who's on guard. Not without taking an Opportunity Attack first.
Make maneuverability matter. A spear has great reach, but once combat is close you can't parry blows with it. Drop it, and draw your sword.
Anyway, that sort of thing. It's not an *extensive* weapon list, but it is an *interesting* and *meaningful* one. IMO.