I wouldn't. The problem is that Magic Weapon and their ilk can be precast before combat, whereas DoTs can't.
Compare with Greater Invisibility instead, GI means you're not doing damage first turn, but you and your party are harder to hit, and hit easier. Compared with "more damage if it lives", I know which I'd pick every time.
The problem is turn based combat is heavily weighted towards nova strikes.
It's entirely dependent on the amount of damage (and possibly the number of targets). Would you rather do 1dN, or 1dN every round with a single cast? Unfair comparison? Unbalanced, of course, but my point is that it's possible to design a DoT that's
better than an instantaneous spell, and it's possible to design one that's worse, so theoretically there's one that's about equal (again, factoring in that you don't know whether it will actually turn out to be better in any given case.)
It's really just a matter of designing something in which the potential benefit seems on average to outweigh the opportunity costs.
How about:
As a bonus action you may place a curse on a target that causes 1d4 damage every time it makes an attack or casts a spell. Requires Concentration.
Conflicts with Hex, and does less damage, but if it's "free" then maybe it becomes a good trade-off to take slightly reduced damage but free up both a known spell and a spell slot.
EDIT:
Actually, I'm starting to like that a lot:
Starting at 1st level, as a bonus action you may place a curse on a creature within 60' who you can see. If the target fails a Wisdom saving throw then every time it makes an attack or casts a spell it takes 1d4 necrotic (psychic?) damage. Requires Concentration, lasts up to a minute, and you can only have this curse on one target at a time. If the target moves beyond 60' or out of your sight the curse ends.
Too powerful for 1st level? I could make it the 6th level ability.
Two options:
- Char mod/short rest
- Damage scales at levels 5, 11, 16 (bigger die or more of them?)