It is odd, isn't it? I only know people medicine, but I have to imagine that the reason staples are used in veterinary medicine is the same...
The bottom line is - using staples to close the external incision line is quick and simple. It's so much easier to staple than stitch.
One advantage might be that closing the incision with staples shortens the time under anesthesia.
They do look like they could pop right out, but they are actually harder to remove than sutures.
Awww, I was SO nervous when mine got spayed and was home healing. I felt so bad for her. Try not to worry, things heal in much the same way no matter how the incision was closed.
Sending healing vibes