Because they had to save the PS3. Obviously they only have so many resources and they devoted the majority of them and the majority of their executive attention towards their home console brand. Had they not done this you would be probably been writing about why they didn't save the PS3 whilst ignoring the PSP like people do here because handhelds just aren't seen as important here.
So whilst they abused the PSP brand they did it to save their more important home console brand. They might regret it or they might not it depends on how the handheld market develops over the next few years. Apple has made more profit off handheld technology than Sony has possibly for well over a decade.
Tease.







