While there where mistakes, I don't think it was possible for Vita to live up to PSP's success.
PSP came out at a time when there was no smartphones, and people were just now embracing iPods over those giant CD players. Basically, PSP successfully merged home console level gaming with that of a portable multimedia machine most people hadn't heard of yet.
When Vita arrived back in 2011, that gimmick was dead. We now had everyday devices that could connect to the internet, play games and watch videos. Vita also had the double whammy of promising PS3 graphics on the go, but that also meant the budgets exploded with it. Any developer could take a risk on PSP and still make some money back because the games were cheaper to make, and could be ported to the PS2. With Vita, the installbase was far too small to justify these serious AAA projects and once PS4/XBO came out, there was no way these games could be ported without looking technically worse in comparison.
Vita was doomed from the start. Sony had to choose between making their home console succeed or their portable one, and the choice is now obvious. When you look at Nintendo, they were going in the inverse direction. Wii U was an absolute failure whereas 3DS still kept them a float. So with Switch, they just doubled down and became a handheld developer that can be plugged into a TV.
As a hardcore gamer, PS Vita was a dream come true. But I could also understand why it seriously lacked casual appeal. Why drop $250 on this thing when the phone in your pocket now offers similar functionality? There where specifically games like LittleBigPlanet and Tearaway that were made for Vita to try and address this issue but it's clear it didn't move the needle in terms of success.