Vita's lack of 3rd party support, is due to a lack of support from Sony. Why would 3rd parties invest in a platform, if the platform holder has abandoned it.
Sony had a goldmine on their hands with Vita, but they went the wrong direction. Instead of doubling down on Vita, and releasing yearly revisions, they dropped it in favor of Xperia. Worst decision in the history of the company. Xperia has lost Sony twice as much as the PS3 stumbles to date, and is continuing to loose them close to $1 Billion a year.
If Sony had followed through and delivered a 4G Vita Phone, instead dropping the Xperia line, they would be in much better position today. With 4G Sony could have delivered the first device to offer Console level Online Gaming on the go (Something we still don't have yet). Take that $5+ Billion in losses from Xperia, and turn that into Games, OS Improvements, and Yearly Vita revisions, and Vita would have been the most successful Mobile Gaming device ever.
Sony only has themselves to blame. With the right moves Vita could be sporting a userbase well over a 100 Million. They would be the defacto place from Console gaming on the go. 3rd party games would be in abundance. Instead they have completely failed. Vita and Xperia are both dead, and they have a massive up hill battle to regain any footing in the Mobile space.
On the bright side. With Vita and Xperia's Failure, it opens up the door to a PS Mobile device based on X86/Radeon, which would be able to offer a unified OS, Games, and Services with future PlayStation Home Consoles. A future PS5 Portable and PS5 Phone could run the Same OS and Play the same games as the Home PS5. This would mean full support of every AAA 3rd party game. With a unified ecosystem of devices, it would be much easier to support than had PS Vita succeeded, as they won't have to develop for X86 and ARM, and potentially multiple GPU's as well. All in all Vita's failure could turn out to be a blessing in disguise.
The only question that remains. Will Sony capitalize?
Dude literally no one wants that except for you. There's a reason both Xperia play and the 3g Vita were massive duds and doubling down on that idea would just cause further losses. Hell why is this even relevant here this thread is about 3rd party support