This is just one of the many plot holes and deficiencies of VOY (like how uneducated brutes like the Kazon, who can't even process water, are able to be a space-faring race, much less a threat to species who have mastered basic industrial age technologies).
(More) Ethical Alternatives
Given the technological capabilities of the Vidiians, it should have been possible for them to find far more efficient/ethical alternatives to organ piracy:
- Artificial organs and cybernetics: Vidiians are overall about as (if not more) technologically advanced as the Federation. Hearts, livers, kidneys, lungs, and even skin can be replaced with synthetic alternatives: artificial hearts and lungs already exist (although artificial lungs are currently rather bulky and are worn in a backpack connected to a large portable generator that has to be towed around by the user), and dialysis machines likewise replace kidneys, and similar machines are being developed for liver functions. Data himself uses bioplast sheeting which behaves much like human skin.
- Biosynthetic organs: stem cells are currently being used to grow all sorts of replacement organs and limbs, including noses, ears, hearts, and livers. While embryonic stem cells might be controversial to many; recycling embryos (ones which have 0% chance to ever become a human being and are otherwise simply discarded) from fertility clinics is certainly better than killing people. Given Vidiian technology, it should be possible to harvest a small amount of stem cells to use for mass production of biosynthetic organs. Adult stem cells from other species can also be extracted without harming the donor (and possibly even in exchange for financial compensation).
- Organ farming: Given that sapience or even sentience isn't a requirement for donor species, there's no reason why the Vidiians couldn't simply raise domesticated animals to use as organ donors. We already do this with pigs, and given the Vidiians' genetic engineering technology (which allows them to make almost any species' organs compatible with their own), there's no reason why they should need to extract organs from sapient species. In fact, they could even genetically engineer a new species solely for organ farming: 10 arms, 10 legs, 5 hearts, 5 livers, 10 kidneys, no brain. It sounds creepy and unnatural, but it's no different from growing artificial hearts from stem cells seeded on an extracellular matrix—you're simply substituting biological structures/processes for synthetic scaffolds and other in vitro technologies.
- Therapeutic Cloning: What better source for donor organs than a clone of the patient? This is another controversial topic, but it's still infinitely better than the solution which the Vidiians have settled on.
As far as the threat of replicative fading or infection of replacement organs, these are easily solvable problems with the advanced technology the Vidiians have at their disposal.
Firstly, sequencing the DNA of every Vidiian during the early stages of pregnancy or extracting seed cells from the early zygote would eliminate the problems of copying errors from cloning or genetic damage from the Phage. Individual stemcells can already be extracted without harming the development of the embryo, and it's already common to sequence embryos from in vitro fertilization before one is selected for implantation. One or two seed cells could be grown into thousands, screening out and discarding any cells which contain significant copying errors. Or new cells could be created artificially (via artificial gene synthesis) using the genetic data sequenced during pregnancy.
As far as phage infection, I'm sure the Vidiians are capable of producing clean rooms and employing the same type of contamination control and infection isolation techniques we have today. If needed, all interactions could be facilitated via remotely controlled robots. Or better yet, the Vidiians could simply outsource to or hire other species to man these organ production labs/farms. The Vidiians could then focus all of their economic resources on producing starships, weapons, or other manufacturing, and trade these goods or their medical services with other species for fresh organs.
So why do the Vidiians resort to organ piracy? Well, the only logical explanation for that is that their society has outlawed all of these more ethical alternatives, and black market organ harvesting arose to meet the demand. Though even this explanation is pretty thin...