Well but people tend to think of darts like used in the game at the pub,
they are not, instead they are in fact short spears. You could melee a bit using them in an emergency.
Obviously the romans invented and used them, google plumbata. From the plumbus = lead (Pb) and what I see in the google pictures and already read somewhere I conclude that these were weighted with lead.
That's true, but darts are not melee weapons. They are ranged weapons as categorized in the PHB. Ranged weapons use DEX modifiers by default. The wording on finesse changes that to allow for STR in an odd way.