If Sony were to create a reasonably priced handheld, with the same core architecture and API of PS4, as well as supporting the system with appropriate software and either a built in HDD or cheap SD card support it would sell incredibly well.
TBH the issue with 3rd party support is no different for Sony in the portable space, than it is for Nintendo in the home console market, if Sony makes games targeted towards the western market, that sell then 3rd party developers will flock to the platform.
3rd party supports platforms that will sell their games, if Sony created a portable platform with unique titles that appeal to the 3rd party market or they made a handheld that made allowed simple cross-play and porting a reality then there's no reason why a dedicated gaming portable can't carve out a decent chunk of the mobile gaming market.
Hell Sony are probably in the best position to appeal to 3rd party, because it's already proven that they can make western focused games that drive the 3rd party audience towards their platform and Playstation is already synonymous with video gaming as people know it today.
The market exists, it's just that no one right now is properly catering to it in the way that those platform holders are towards the home console or PC user base.
