PS4 should run Android apps... yes or no?

For:

A large part of the next console generation will be about non-gaming functionality.

Sony is the only one of the big players without an app eco-system. e.g. Microsoft have Windows + WinRT + WP8 + Xbox, Apple have iPhone + iPad + Apple TV and Google have Android + Google TV.

The ability to run Android apps would give the PS4 a jump start in this area.

A secondary positive outcome is the potential for a lot of creative indie games and emulators that otherwise wouldn't find their way in to the PSN

Against:

The potential for a lot of not so creative indie games and emulators that otherwise wouldn't find their way in to the PSN

Sony give up a lot of control and lose the ability to curate.

There is the potential that a developer may simply have PS4 owners use a standard Android app instead of developing an optimised 10ft experience.