No, Handheld gaming is not going anywhere. The most that will happen is traditional Handhelds will see a price structure and delivery change.
Likewise, Consoles are not going anywhere. Console quality titles suck on handhelds and vice versa, there will always be a place for both.
Ten years ago, people speculated that consoles would kill PC's. This has not only *not* happened, the PC is entering a new renaissance.
Using Sony as an example of a proper handheld is also a mistake, as Sony has *never* understood how to sell a handheld game device.