What I meant as an oversight is not that the lance requires 2 hands when not mounted (I have no issue with that), but that it doesn't have the heavy property when not mounted. And as Undrave pointed out, a halfling or gnome can use a lance with no penalty, but if they use any type of polearm, they attack at disadvantage. So I think it should also give the heavy property just like any other polearm when not mounted.
That makes sense, and I don't disagree. But having it be one-handed but needing two hands while not mounted also means it interacts with other features oddly:
It can be dual-wielded with a feat, but not used for a power attack (or cleave)
It can be used by 1st-level hexblades with the Hex Warrior feature, even though glaives cannot
It works with the dueling fighting style, and potentially two-weapon fighting, but not great weapon fighting.
While none of these things are mechanically a real problem (except maybe highly incentivising 1st-level hexblades to use lances while on foot), they all
feel wrong. Because the fantasy of the lance is much closer to a greatsword or greataxe: it's about big, mighty blows that fell a giant, not deftly finessing one or two to numbly cut through the battlefield.
Then again, I could say the same thing about halfling lancers - it's not that they do too much damage, it's that the feel silly. (especially when dual-wielding)
(I'm not arguing that dual-wielding lances is impossible in the real world, although I would argue that it doesn't fit in with lance tropes.)