There is also the Point that a +1 Weapon, gets +1 by a magical enchantment, this also means the weapon it self is magical.

Imps for example have resistence to fire... AND nonmagical Damage. If you fight these 10HP imps Lv 1 you are not rolling poorly. They are just resistent to your damage.
Later you will probably meet Werewolfs, Ghosts and Vampires that are completly immun to nonmagical damage.

So a magical weapon is important.
Additionally a Lv 4 Character with 16 str for example.

He gets +3 from strenght, and +2 from Profiency. That means as a total he has a +5 to hit. With a Sword thats a 20% greater Hitchance.
Additinally you get "Multiattack" at Level 5 Combined with Haste Potion and Actionsurge its not just 1 extra Damage per turn, its +5 Damage...so jeah it really adds up.

In Normal DnD +2 Swords are basicly some of the best weapons you are normally likely to find, unless you get some epic story sword.