Everyone against this definitely has good points, but I think the point of a mass delete option is to more easily get rid of common pets that don't have much value but are present in bulk—not to delete super rare pets that people typically don't have in bulk in the first place. I believe a bulk delete option wouldn't negatively effect the rare pet trade at all. If a player really wanted to delete one of their super rare pets, they can do so already.
Having hundreds of common/vc/omgsc with low demand can be quite a clutter because they are hard to trade away. Even when they are donated to the pound, they are often chosen last. These pets don't really go anywhere, so I think a bulk delete option would help with pets that have a low demand low supply problem