A total of 22 games sold over a one million copies on the PSP. The number of PSPs sold is irrelevant, the number of games is what matters because most consoles are sold at cost or a loss. People bought the PSP because it was great at running homebrew games. Sony locked that down on the Vita and it sold way worse.
And then you provided a list of other failed attempts to get a piece of the Nintendo handheld market. Just because it was released doesn’t mean it was successful. If the PSP or any of these other handhelds where profitable they would of had successors sold today.