Parent and Child parking spaces didn't exist when my DCs were little - and out of town shops with their own car park didn't exist either. So, the supermarket was in the high street and the car park (a multi storey) was about 300m from the shop.
Car seats for babies didn't exist either, so we had to transport in a carry cot (basically the top half of the pram) almost filling the back seat. Upon parking, baby had to be removed from carry cot and manoeuvred into a sling, then carried down 4 flights of stairs (or wait ages for the lift that smelt of wee and vomit) and 300m along the pavement to the shop, lugged around the shop, then back to car park with the shopping. Then the trolley had to be taken back to the shop.
By the time we returned to the car for the 2nd time (minus the trolley) baby had often filled his nappy and needed changing. No toilets in any shops in those days, let alone changing areas (though we were campaigning hard for Mothercare to install changing/feeding areas, they hadn't yet materialised). So baby had to be changed in the car, on the front seat. No disposable nappies in those days, so we always had to have some spare terry squares and a plastic bag to put soiled nappies in (which were of course taken home to be sterilised and washed).
So, that's how it was not so very long ago! Things are so much better now for parents with young children.
But I do take the OP's point. Parent and child spaces are surely not intended for any age of child, but only babies?
If it's any age child that can use them, I could take DS (who's 36) with me next time I go to Tesco and park in a P&C space. We are a parent and child, after all!