Completely random runs are probably gonna be pretty tough, because you could end up stuck with very loopsided party compositions (e.g. too many attackers, too many tanks, too many mages), or lack certain niches (e.g. healer, de/buffer, ailments, defense piercing).
Of course you can probably still clear all the content in the game by grinding/overlevelling, but otherwise I think something like 6-8 random chars with the rest being picked consciously would probably be a better experience.