May I ask why you need the old electrical? I seriously doubt there is much from it you can use, and the new pool MUST be up to modern code standards.
I would abandon anything left form the old pool and start from a clean slate?

Is your electrician familiar with wiring/bonding in-ground pools?

Pools are a nightmare of rules in the NEC.

We can't guess what the sub panel is for. It might be anything.

As Brick implies there are a whole lot of rules with regard to electrical and that big tank of conductive solution you're going to immerse your family in. This includes bonding equipment and exposed metal, GFCI, wiring installation procedures, clearances between receptacles and lighting, etc... This is not really a DIY operation.

OP states-"I am installing a new ABOVE GROUND pool"

Most of the ABOVE GROUND pools (depending on size) use self contained, fully insulated filters that run on 120VAC with a standard plug in type cord.

There are not heaters, pumps, etc that are used and would require bonding, etc.

Lets make sure we are all talking about the same thing-this is different than an in-ground pool.

It may be that the (15A/20A) 120VAC outlet is what was used for the previous ABOVE ground pool. I agree that new would probably be better.

Admittedly, there is still the potential for shock and electrocution, but let's find out what is being proposed first!

"Most of the ABOVE GROUND pools (depending on size) use self contained, fully insulated filters that run on 120VAC with a standard plug in type cord. "

Quite incorrect. MOST above ground pools have typical pumps with 3' cords and grounding twist-lock plugs/receptacles.
Let me correct that, MOST properly installed pumps near the pool wall (as is typical for an above ground).

Also, there are plenty of other REQUIRED codes with regard to above ground pools, such as bonding.

Pools require insulated grounds all the way from the panel IIRC.

No NM with a bare ground conductor.

NM is allowed for portion of wire inside the residence for circuits feeding a pool pump.

Above ground pools have little difference than inground pools as far as the code goes. They are both "permanent" installations in most cases. Bonding requirements are the same and just because your pump is cord-and-plug connected only modifies its bonding requirement not eliminating it.

Petey is right, the latest code makes an exception for interior wiring of motor circuits that allows it to be bare within a sheath.

It's probably just a symptom of the backwards mentality where I live, but "most above-ground pools" in my hometown are made by Intex, purchased from Walmart, are made of thin plastic with an inflatable ring at the top, and include a pump with a standard 120V 15A grounded plug which most people plug into some scary conglomeration of extendo cords and adapters...

"Nightmare" applies!

Ron, I have known this part of the code to be there for quite a while. It's definitely not the latest code.

Funny thing is, if you are feeding a pool sub-panel or light then it HAS to be in conduit the whole way.

It changed in 2005, I guess it wasn't all that recent.

I know I am nit picking, but it was added in 1999, then changed to 680.21(A)(4) in 2002.