I know UMD isn't remembered all that fondly, but I do think they gave the PSP a weird added appeal that Vita didn't have. You could play GTA, GOW, Metal Gear, FF and other games portable for the first time, but you could also watch films on something that wasn't a dedicated media device like an Archos media player or whatever. And also worth noting is that it came out a few years before the iPhone, YouTube released the same year as the PSP. Facebook hadn't began fully rolling out to non-students until the following year. Next to the Nintendo DS, it seemed lightyears ahead in terms of capability - without Sony would we have gotten the DS Lite? We might not have gotten a rushed first gen ugly-DS actually! Nintendo definitely had a good strategy keeping the price low, releasing popular games (including the Touch Generations stuff), but Sony made them work.
The Vita released in to a totally different world in comparison. Android Phones, iPhones, iPads, Netflix, strong competition on the home console front from the 360 and the Wii, and probably a huge diversion of resources to ensure that PS4 would do better than PS3.
I don't actually believe that they're walking away from handheld gaming for good... I think as others have said, maybe they see a future in PS Now and Remote Play, whether they release a device for those or not, or just exploit other hardware... but I think they probably see streaming as a big potential market disruptor too. It would probably be crazy to reinvest heavily in a dedicated portable platform if we're on the cusp of having the ability to take hardware costs almost completely out of the equation. I've no doubt Nintendo will be thinking about that and how they can either join in or somehow continue to stand out when it arrives.
