Remember in the lead up when people were convinced the original PSP was going to be the biggest thing since sliced bread? Sony even dubbed it "the Walkman of the 2000s"
The painful irony is that Nintendo had more faith in the PSP's success than Sony.
The GBA was selling like hotcakes yet Nintendo was willing to kill it off (gradually over the course of 2 years) and get the DS out early.
In some ways it's like a repeat of Bandai's WonderSwan Color and the early GBA launch in Japan (had Bernie Stolar, famed Saturn-killer, not have landed at Mattel who were to sold the WonderSwan overseas, it might have very well have posed an existential threat to Nintendo)
But then what did Sony do?
They at least hired the Bleem emulator developers to really bring the PlayStation 1 to the handheld world, but it was just that.
No thought put into supporting it with experiences tailor made for handheld gaming, no long-term strategy, nothing...
Even though it was far better placed against piracy than the DS, Sony dropped the ball there too. And their idea of "solving" that problem on the Vita was to punish consumers with even more expensive proprietary memory cards 33% as expensive as the console.
I think the most clever and crucial decision Nintendo has made was getting Monster Hunter exclusive for their platforms and most especially the 3DS. That move alone i think was enough to suffocate the Vita before it even learned how to breathe.
Sony didn't deserve the Monster Hunter franchise.
They were acting cocky and arrogant.
They even announced a Resident Evil on behalf of Capcom without them knowing about it or developing it.
The visual novels that propped up the PSP in its later life were being rejected in 2006 (Sakura Taisen 1+2's English version) for not being "true games".
Then by sheer happenstance
Monster Hunter revived the ill-performing console in Japan and became its killer app, and of course Sony had to be assholes about it somehow. So they offered a program to port major PSP games to PS3 with HD textures and Monster Hunter Portable 3rd would be one of its first results, and Capcom loved it since it would mean a console version with online and English (since they weren't willing to release it on the PSP overseas over piracy concerns) and Sony was all cooperative... until the eleventh hour when they did an about-face and
rejected the HD console version, because "its visuals are too shitty to be on consoles and it's more suitable for handhelds".
Of course this fact, and how they had Capcom panicking and trying to solve the solution to no avail, didn't arrange their relationship. Since the only other option was Nintendo, and their newer devices (after DS) were viable for Monster Hunter, and Nintendo didn't have any such restrictions (and indeed the Wii U and the Switch received direct handheld ports this way) it was an easy answer.
It serves Sony well that they were scrambling so much after this misstep (indeed their disregard for developers welfare already caused more than a few to go under) for a new Monster Hunter, an easy cash cow they squandered just like that because of their massive ego, to justify their Vita they relied on Namco's God Eater series and then started pumping out their own Monster Hunter clones (Freedom Wars, Soul Sacrifice) and only solved this situation with a massive bankroll that came with a contractual obligation to skip the Switch specifically.
That also had the nice side effect of no more multiplatform games (PS3/PSV/PS4) skipped or rejected just because that's what they are. Imagine the Romancing SaGa remakes (used by Square to catch up on the series for English audiences, and gauge interest for the Vita game) skipped for being phone games with visuals "unbecoming" of consoles.
