Let me ask another pertinent question:
How can tablets like iPad/newer androids manage to multi-task (albeit limited) when the total amount of RAM being 1GB? On the PS4, last I checked, there is no true multi-tasking (like browsing and gaming at the same time with a divided screen or browsing and watching netflix etc simultaneously). In general, most people keep multiple tabs and multiple programs open (not background stuff) but seldom use more than one thing at a time. The most common combination is listening to music along side browsing, editing pictures or the like.
Are we really expect people to do more than 2 different things at a time (360 attained cross game, chat and custom soundtrack simultaneously with a meagre 32MB OS)?
Yes, I am keenly aware that they use their own mobile apps that are less resource intensive and occupy far less space once they are relegated to become a part of the background process. So the question is, why can't we have it for PS4 (and xbone) for that matter?
The only feature innate to PS4 which could be a resource hog is remote play via vita but even then, PS4 won't simultaneously be playing one game while streaming another.