There are good pets, bad pets and pets that have been cursed by developers.
Their abilities are arranged that way the cooldowns are overlapping, what cause a lack of choice or straight unplayability.
Perhaps the most known example is Bone Serpent, but that's a drop in the ocean.
Ever tamer pets can suffer from that, like one of the moths or Mirecroak since infamous change to Frog Kiss.
I'd tell there's a sliding scale, but that would probably not encourage to discussion.
Well, look at Mini Mindslayer. Since 7.0 you have either Inner Vision → a 1st tier ability → Inner Vision → Interrupting Gaze → a gap, or a 3rd tier ability → Amplify Magic → Mana Surge → Amplify Magic.
Pygmy Cow is great for Celestial Tournament or as a scarecrow to Fragment of Anger, but can hardly do anything else.
Enchanted Pen is forced to use Quills.
Can you recall other pets with that problem? Maybe there's a particular one that makes you angry/sad because of the necessity to put it among various "useless" pets? Let's see.