ok, counterpoint - rapiers exist. the average weight of a rapier is about 1 kg - the average weight of a longsword is about 1.1-1.8 kg, but we'll settle at the median of 1.5 (well, it's actually 1.45, but i'm choosing to round up, you'll see why in a second). it's estimated that having a second hand on a melee weapon increases your effective strength with that weapon by about 50% (this is why 3e let you add half your strength again to attacks made with a weapon you were wielding with two hands). 50% of 1 kg is 0.5 kg, and 1 kg plus 0.5 kg is...exactly 1.5 kg. coincidentally, this also works almost identically with dnd's weapon table - rapiers are 2 lb, longswords are 3, you can do math. it'd be reasonable then, i'd say, to consider two-handing a longsword (or, at least, the kind of longsword dnd seeks to represent and lighter ones) to be approximately equal to using a rapier in terms of finesse.
or, in other words - yes, two-handing a weapon is meant to give you leverage. for at least longswords, that leverage significantly lessens the need to be strong in order to fight effectively with it. hence, two-handed finesse weapon.