Archers don't need two bows but they sometimes need a melee weapon so this system works perfectly for them. But melee characters do need different damage types, while a bow slot is absolutely useless for someone with a high Str and low Dex.
I think that a generally melee character has just as much requirement to sometimes attack at range as an archer needs close combat capability. Eg sometimes enemies might be too far away to reach, and they might prefer to do some damage at range rather than just dash, especially if the enemy is on a hard to reach ledge. Or they might want to hold a good position and do damage to weaken an enemy coming to them. And conversely an archer might prefer to disengage and regain range and positional advantage rather than swap to melee.
I don’t think, that is, that being able to adjust to handle different ranges benefits archers any more than strength based melee characters. It is more useful to characters who are specced to be able to cope as well both at range and close up, but as building a character this way would often already involve sacrificing potential benefits of specialisation I don’t see this as balance-breaking.
Okay, a strength based fighter would more likely use throwing weapons than the bow slot, but they have the same ability to freely swap to throwing as to using a ranged weapon, it’s just handled differently in the interface. And an archer would be unlikely to want to throw a weapon instead of shoot, so the weapon throwing functionality no more useful to them than the bow slot is to strength based fighters, retaining parity.
Ok let's put it this way: if the slots were free to equip anything you want, how would this more flexible system make it worse than what the game has now?
As I said, not a hill I’d die on. But if melee characters could use a weapon slot to freely swap to do a different damage type once per turn (as well as having the ability to attack at range by throwing weapons unless that is changed) this would seem to me to tilt balance in their favour by giving them an advantage that an archer wouldn’t share, particularly if there remained only two weapon slots plus throwing weapons as now. I’d therefore prefer to keep it so characters need to use an action to swap melee weapons.