I suspect it's because the "rare" pets that are on the BMAH are usually available on the regular AH for similar prices. I've often seen BMAH pets bid up much higher than their normal AH prices.
I've bid on just about every category of item on the BMAH. Anecdotally, I would say legacy items (T3 mostly) and mounts are the most popular. The Unclaimed container also does quite well, but I assume that is people hoping for mounts.
Blizz BMAH Poll
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Necia
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Not sure it'll make a big difference but saw rare pets were an option. I was a little surprised at the low pet vote too, so just sharing in case folks didn't catch it on the front page. 
[url=http://us.battle.net/wow/en/blog/19816679/poll-the-black-market-auction-house-7-6-2015]Blizzard: Poll the Black Market Auction House[/url]
[url=http://us.battle.net/wow/en/blog/19816679/poll-the-black-market-auction-house-7-6-2015]Blizzard: Poll the Black Market Auction House[/url]
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Voskres
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Re: Blizz BMAH Poll
If it was something no longer available, then perhaps it would do better (Bat from Kara, Olympic dragon, Gladiator murk, etc).
They went quite a ways to kill the 3rd party gold trade and they could do a number on 3rd party pet trade by putting them on BMAH.
They went quite a ways to kill the 3rd party gold trade and they could do a number on 3rd party pet trade by putting them on BMAH.
Re: Blizz BMAH Poll
Availability is the main thing. You can get all of those pets from the AH if you're patient, while the mounts and the transmog gear for the most part you simply can't buy. And trust me, a person can only run certain raids so many times before they go a little insane and would rather spend gold on the BMAH. Oh Kael'thas... so much talk and wait for so short a time fighting.