Professional release programs are run from a scientific perspective. Any animals they release are carefully screened for problems or genetic abnormalities. It's also only done with endangered animals, or generally with animals that range a long distance such as large mammals and birds that need to be relocated.
Adding new genes to the gene pool in a locality can damage the population, or species in animals with small ranges. Often times, subspecies are poorly defined, or definitions change, and introducing a new subspecies to an area could result in hybridization, which is detrimental to the species.
Parasites can be found in food items, from human contact, or from contact with other animals. There is no such thing as a sterile captive setting, even if possible, it would kill the animal. Also, parasites aren't always obvious, and often times don't always harm the animal. In many populations, certain internal parasites are considered normal. Regardless, introducing these to an area they don't naturally occur can have a negative effect on other animals in the ecosystem.
It's also illegal to release captive animals in most states for these reasons.
While eggs are less likely to carry parasites than adults, it can still happen, and even if none of the other problems don't occur, the potential far outweighs the benefit of quickly getting rid of the animals or eggs.
