A few kids? That appears to be a 15' diameter pool, about 4 feet deep. Thats over 700 gallons of water at 8lbs per gallon or nearly 6,000lbs of water. Stop pretending its an inflatable kiddy pool. Your neighbor would prefer if it didn't collapse and flood his basement. If you are in a more northern region, the footing needs to be below the frostline. Here in Kansas thats typically between 3.5 and 4 feet. Finally, blame the city, its their requirement.
Whoa, whoa, whoa...engineering is coming up with a solution to a problem. Making things go. Engineers design things, often to the local code. What you are doing is called construction, usually carried out by contractors, and more specifically, you are excavating for pier foundations. 52 inches sounds deep, and maybe in your location, thats the frost depth. I did this for the deck around my pool, 12 inch round footers. Yes, it's a lot of posthole digging. It was much easier with a 1 man auger. Usually, if the rock is soft enough, ya break thru the rock. If the rock is big enough, you drill in a dowel or two and pour at that depth. This can all be skipped tho, as well, by using at-grade, precast footers. They even have the brackets for the posts set in them. Ya use the engineers plans, and substitute the footer. Save ya a bunch of time and material.
It’s crazy to use 24” diameter footers for a pool deck. We do this for a living and are not complaining. I just think that using 13-24”x48” post holes is way over kill for this😂.
You wish. The “Easter bunny” would never leave that there if the kids didn’t find it while hunting eggs. That would be a nice find. But because you’re working on someone else’s property, the right thing would be to give it to the owner of the property.