I think it's a bit of a shame, almost criminal that there isn't a simple elemental-damage-add weapon cantrip spell. Add like a d4 or d6 fire/ice/thunder/acid/lightning to a weapon attack, like a scaled down flamestongue/frostblade weapon for eldritch knight/hexblade/ranger/paladin types.
While I agree it would be nice, extra elemental damage per attack is actually pretty strong in terms of DPR. Generally, a +1d4 and +1d6 damage die sits right on either side of getting a +2 magic weapon. The +1d4 is closer to the +2 weapon than the +1 weapon.
The Magic Weapon spell is level 2 (castable at level 3 by a full caster, or level 7 by an Eldritch Knight), and makes a weapon a +1 weapon. Upcasting to a 4th level spell (castable at level 7 by a full caster, or level 19 by an Eldritch Knight) makes a +2 weapon.
Aside: The Eldritch Knight might get access a level or two earlier, given the changes to the spell progression table in 2024 that have been talked about.
Brainstorming a little, I'd first consider making the cantrip provide an extra +1/2/3/4 damage at levels 1/5/11/17. Flavor it as an elemental effect of the appropriate damage type. Require concentration?
The problem is that that's still a weak 1d4 at level 5, a weak 1d6 at level 11, and a weak 1d8 at level 17. Will that skew the balance of things too much? Though since it's a static boost and not a die, it won't be affected by crits, which limits it a bit more.
I dunno. There's so little wiggle room between magic weapons and elemental dice and leveled spells, it's hard to say if a cantrip can work in there. Maybe just +1 damage at level 1, and +2 damage at level 11?