My two cents as someone who's only found CS a few months ago (through the Dragon Cave forum no less): in the beginning, my main collecting option was the free adoptions. I had no pets to trade with, and so all I could look for was pets that people no longer wanted or were quitting, and build up my own collection slowly.
I'd like to collect all eventually, but I also am pretty sure I'll probably never get all the old rares just because I just don't have the mass quantity of rares to compete. Which is fine (I'm not lamenting, just giving a newcomer's POV). I'm not greedy just because I want free pets - I am adopting unwanted pets, and I don't have the time-build-up here where I have a ton of old rares to trade for that one dream pet from long time ago. Unless you want like 100 uncommons and like 300 commons (that everyone already has) . .
The fact is, I don't see much point in the delete button, especially when you have other options to clear space. Besides, a bunch of people have to delete the same pet in order to change its rarity, and unless it's like some flashmob-level coordination, I'm not sure how it'll happen.
TL:DR There will always be newcomers who don't have those unwanted pets and no way initially to trade for them. Maybe they can build up to get them later, but there's always someone who wants that pet, even the most common ones. Think of the pets!