That's a rather offensive and broad generalization about pet ownership.
And it is hardly the power to take life away. That is a rather flippant view of being faced with the decision to euthanize an animal. Is it humane and decent to let an animal that is suffering and dying just lay there in agony until it dies? I think not. Killing an animal because it is two headed and may not live a long life is most certainly not the right thing to do. It does deserve a chance to make its way, but, if an animal is suffering, is going to die, and there is nothing you can do to help it, it is a rather unselfish and loving thing to put it out of it's mysery rather hold on to it as long as you can because YOU cannot bear to part with it. That is seems more selfish and controlling to me than to decide to euthanize a suffering creature.
It also seems to me that having a desire to obtain and own all these poor creatures that have these mutations like being eyeless and two-headed is more of control issue than deciding to euthanize an animal (for the right reasons of course).
I am not trying to be judgemental. If people want to collect these unfortunate freaks that have an uncertain future, that's fine but I can't see condemning someone and calling them controlling for not wanting to let their animal suffer any longer than it necessarily has to and in the same breath collecting these animals who will have a very compromised life just because it is cool to have these oddities (and not consider that playing "God".)