Plus, you can summon and dismiss them, unlike RL pets.
I'm not sure about the time limits for summoning though. Possibly it was introduced to prevent pet spamming / use as signs, so it doesn't necessarily emphasize the magical nature of pets.
So all the times I said "You can go now", or "Go Away" to my dog, it didn't really leave this plane of existence? Well, there goes that theory. Now to find out where she really goes, preferably without leaving my comfortable chair.
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Other then that, interesting.
If you assume that that for each second the pet is on our plane it takes some strain from being summoned from where ever we summon them from and away from their natural place in things, or that we have to concentrate to keep them here instead of there, then it makes some sense that they could only be here for so long, a time limit that would probably be effected by will.