FF7 did get an official PSN release playable on PSP. You could play FF1-9 on PSP by the end of it's life once the port of the DS version of FFIII arrived. There

FF7 did get an official PSN release playable on PSP. You could play FF1-9 on PSP by the end of it's life once the port of the DS version of FFIII arrived. There was also a PSN release of the PS1 version of Chrono Trigger, which is actually how I played through it (although perhaps on Vita).