The touch of your shadow-wreathed hand can siphon life force from others to heal your wounds.
Doesn't say "exclusively from others". Without casting this spell you couldn't do that normally.
It also says,
On a hit, the target takes 3d6 necrotic damage, and you regain hit points equal to half the amount of necrotic damage dealt.
No qualifiers about the target having to be a creature other than you. It just has to be a creature within your reach.
Also as regards:
As a DM there’s a few ways I’d consider to stop this being entirely game-breaking:
Do you also ban death ward and healing word? What about wizards who dip a level into virtually any other spellcaster or take a feat for a healing spell who can do this kind of thing without even having to make an attack roll or take necrotic damage?