Honestly, I have a few points here:
1) Everyone always uses Garuda forever, because Contagion is the best, period. The fact that she's a caster type is icing on the cake.
1a) Pets should be made more useful in general. Other than adding auto-attack dps and not responding when I command her to use Contagion, I have zero cares about Garuda besides maybe telling her to stop standing in AoEs.
1b) Seriously, how come I have to press Contagion like 30 times before she feels like using it!?
1c) Pet abilities should queue no matter what. I understand that player abilities don't queue unless your GCD is almost up, but you really want me to watch Garuda and tiem my button press with where she is on HER GCD? If I give her a command, she absolutely should execute it at the next opportunity, not blindly ignore my command because hey, she's busy ok?
2) Pet abilities are slow to respond to input, depending on what Garuda is currently doing. She's currently attacking, and it's too long until her GCD is back up? Well, too bad then, she's ignoring your commands. This happens with Enkindle, as well. Every time I'm sitting there hammering a button that won't respond, my dps is facing a steady decline. This game punishes inaction, so making the system such that pet controls are unresponsive is... pretty questionable.
2a) Do you think anyone legitimately uses Garuda's push back ability? Because they don't. Mostly this just goes off because some poor guy has Sic on for some reason. In order for Garuda to push something back (which would be handy in Second Coil, Turn 4, to push golems) she has to a) acknowledge you even sent her a command (unlikely) b) move over to the monster c) finally push it back. Considering anything you'd want to push back (adds in Leviathan, for example) you need to push back VERY QUICKLY, the utility on this ability is basically zero (it would be questionable even if Garuda could push at range, due to unresponsiveness of pet controls).
3) Pets are very boring. Putting what should be base utility of SMN onto a pet is not very interesting when we should be making pets more diverse and interesting to use to begin with. Even tanking with Titan is very uninteresting, as there is very little you can tell him to do since he only has a couple actions to begin with.
tl;dr - Pets are boring, unresponsive, and should have base required SMN utility added to them - they should be unique, interesting, and... useful. Not to mention - fun to play with, instead of mostly ignored (except as a potential hindrance, thanks to them dying and lowering your dps).