Could humanity survive without wild animals?
I don't know but I would hate to have to live in a world that had no wildlife. Every being on this planet has a job and when everything is working as it should we hum along! However man seems to think that they know better and we have proven over and over that we should butt out in most cases! Note the cane toads in Queensland brought there to take care of the rodents in the cane fields. The taipans who hunted the rodents now tried to eat the cane toads and they died as a result of the poison in their skin. Now the true killers of the rodents are dying, the cane toads are reproducing at an alarming rate leaving a trail of dead native animals who tried to eat them. There appears there is no answer at the moment. A case showing we should have left things alone in my opinion!
I wouldn't want to be alive in that scenario but I am pretty certain we will survive.
But not that long . Animals play a big rol in distribution of seeds, pollination, controlling pests and other animal bussiness. Not even to mention the importance of the fish and other aquatic animals. Domestic humans will be able to solve the problem. For a while at least.
A random guess, about half the world won't make contact or see any wild animals today, maybe even this month.