Firstly: It is not the same treatment. There is quite a difference between actually being beside the pet, and just watching it through a webcam, especially for the pet. Some pet's can actually get ill from loneliness.
Secondly: What will you do when x number of pet's get ill? You can't watch them all, the owner might not notice, and then suddenly one day, a boy log on to see to his pet, and find it laying dead in a corner.
Thirdly: I find it morally unjust, a pet shouldn't live in a cage it's whole life, watching a metal piece. Even in pet stores, pet's are put together before bought, but once they are bought they in contact with a human at LEAST once a day. In your idea, they are moved from one cage to the next during their lives, depending on if their owners want them to be with other pets
And, how big of a scale are we talking about here? 10 pets? 100 pets? 1000? What KIND of pets? If you open a website like that, people are gonna be storming from everywhere, be it to have a pet, buy one just to abandon it, or to torture, there are all kinds of people out there.