As I see it the doll has a few key uses: 1) As insurance in case the enemy makes a vital creature invulnerable; 2) Incentive for the enemy to avoid using indiscriminate spells (e.g. Unstable Gas, fire storm); 3) As a way of opening up enemy creatures to damage by self-only creature control (immolation); 4) Amplifying the effects of a single-target spell (by chaining puppets) or - even more so - multi-target spells. 5) Single-target spells which are good if they affect your creatures and bad if they affect your enemy's.
5 is very rare. The only such ability I can think of is aflatoxin, and even then only in situations where you have a damage-reducing shield, they don't, and you have bonds.
4 is not very cost-effective; if you parallel universe a puppet you get two puppets pointing at one creature and a second copy of that creature, so to "chain" puppets you need to fractal or have multiple copies of the card. Once you've done that enormous set-up you can get multiple creatures worth of blessings, plate armors, aflatoxins, quintessences (kind of pointless without also adding damage somehow), powerful results from rage elixir, or potentially some fun with improved mutation. Drain life could potentially be powerful (if a little counter-productive, as it destroys your own puppets after you spent so much effort making them)
3 is potentially extremely useful for the cost, as you can get double the quanta out of immolation and also kill a valuable enemy unit. You can use butterfly effect on any enemy unit as well, which is powerful for entropy/darkness decks (you get a creature with destroy, the enemy loses an ability and gets one they can't necessarily use).
2 is only going to be worth it if the creature has little life or the opponent is using a huge amount of such spells (or if they use poison and you have time to kill).
1 is pretty situational; most enemies you will play don't have any way of making a creature invulnerable. It could be useful for pvp at least.
One question: what does Lobotomize do? Does it remove the voodoo connection before the other creature does, after, or not at all? To rephrase, does lobotomize on a voodoo doll leave you with a useless doll, a skill-less creature, or both?