Good to know! Yes that’s what we plan to use is a plate compactor and go slow and make sure it’s pressed completely before adding the sand on top. Did you use 2” or 3” we plan on doing a sand cove instead of foam.
How are you going to make sure it is "pressed completely". Are you going to use a sand cone or rubber balloon, or do you somehow have access to a nuclear soil density gauge?
All sarcasm aside, you do not, and can not know that it has been sufficiently compacted unless you test it, and you cannot test it unless you know the specific proctor curves of the soil you are compacting.
You stated you are going to put "crushed stone", which I assume is 3/4" clean, and then put sand on top. All of that sand is going wash into the void spaces of that 3/4" stone. 3/4' is a very poorly graded aggregate and has lots of interstitial void space.
You could use QP, crusher run, 2" minus, DGA, road base, whatever it is called in your neck of the woods and would be much better off. QP has a very flat (forgiving) proctor curve and therefor you at least have a fighting chance of getting the compaction right. Without knowing the results of a Proctor test and then an in-place density test though you are still trying to hit the bullseye blindfolded and in the dark - at least with QP the dart board is larger.
Here is the tricky thing. Soils can be compacted to a maximum density only at a specific moisture content. Any more or less water in the soil and you can compact it all day long, and it will still settle once it either dries out or gets wet and gets to the optimal moisture content.
Yes, things can be built on fill. It is done all of the time. I have built public buildings on 10 feet of fill. But it has to be done right. Somebody playing around with a Home Depot rental plate compactor and guessing at if they have compacted the fill enough is not doing it right. The other thing is pools are heavy - very heavy. And unlike a garden shed, are quite unstable. A pool is a big, heavy, bag of water, and the only thing that is keeping it in place is the fact that it is level so that the forces around it are consistent on the frame. Let the ground settle under your shed and your doors may be sticky to open. Let the ground settle under your pool and in your case upwards of 40 tons of waters goes crashing through your backyard. That is why it is recommended not to fill under a pool. The base has to be level and the potential for damages, injury, and even death if a pool lets go are serious.