I don't think the OP gets the "point" of such an account system.
If you were to have a different ID on each system (kinda like a Friend Code), each one would have a separate trophy list, friends list, downloads list, transaction history etc.
A unified system like this allows you to, say, play a PS4 game, then get off your sofa and to a coffee shop where you'll be able to receive mail from all your friends to your PSVita while playing PSVita games, then hop in to a bus to visit granny and play a bit on your good 'ol PS3, all on one account.
Hell, the infrastructure even allows Cross-Buy - some titles can be played on more than just one system, so you can, say, play your favourite Metal Gear Solid 3 at gran's, then transfer the save to your PSVita, play it on the bus back home and then return to your PS4 game.
While doing all this, you're constantly available to your friends, you can continue receiving mail, play online, do shopping, add funds or do whatever you want, all on one account, regardless of the system used.
Arguing that it makes no sense to have one unified account is like arguing that you should have separate bank accounts for notes and coins. All of Sony's current systems are within one ecosystem and they interact with each other using the PSN infrastructure for your convenience.
Your purchases don't go "poof", they're saved on the account. Sure, you can't play PS3 games on the PS4, but neither can you play PSVita games on it and you can't really blame it for it - they're entirely different systems. Ever tried putting petrol in a diesel engine? Not gonna work, even though "it's from the same petrol station you buy oil from".