1) Your pet will attack your current target too if it can attack. It could be that you have a pet who does not attack. Often praise pets (as well as some non-praiseable pets) do not attack your target.
2) You can already pretty much "mount" your pet, by just jumping on top of it
3) Like what OrchidFlower said, additional items on your pets would indeed lag the server further. Besides, that would mean we would have to position items for each seperate pet, because they all have different skeletons if i recall correctly. This looks good on paper, but is a nightmare to implement