Some assorted thoughts.
I think that all the special weeks should go. I thought they were cheap, inappropriate, jarring, and tacky when the devs introduced them out of desperation in Warlords, and I haven’t changed my opinion.
The devs aren’t rewarding pet collectors. They are spacing out the weeks as part of the expected gearing curve.
A significant number of people collect and battle pets. Anywhere between 12% and 25%, depending where you put the cut-off for engagement. That compares favourably with the number that raid above LFR.
The pet week quest, and its reward, are separately and together pretty appalling.
The main benefit of Pet Week, for pet battlers, is not the PvP quest, but the PvE Super Pet XP.
The reward for 5 PvP wins is a Purple stone. You can earn a Purple stone most days by doing two quick world quests that give Charms, and buying the Purple stone with the Charms. It is a complete joke as the reward for a weekly quest.
Compare that with actually getting 5 PvP wins. By definition, the win rate in PvP is 50%, so on average that would mean 10 battles. Assume 5 minutes per, including queue time if you are lucky and the queue is really hopping, and you might say you should get it in an hour. At least, people who never tried it might think it would take just an hour.
Imagine a quest for 5 duel wins, and someone who has rarely or never duelled, and probably with weak gear, going into the queue against the regulars. Yeah, it’s like that. If you haven’t at least done a lot of homework, you’re probably going to lose those ten battles with nothing to show for it. I might get it in an hour, if the queue co-operated - whish it probably wouldn’t. But I’m not going to bother; the reward is trash to me. But an optimistic beginning battler is just going to lose the will to live.
There’s a whole thing about why pet PvP is bad. Here’s a thread about it, for anyone who wants to get a start on understanding why: Crank it up for the battle pets?