The only reason PS2 appealed to all audiences is because the system had a great variation of third party games and those games did most of the job.
I doubt that first party PS2 games played a big part, according to VGC, the best selling first party game for the system is a "casual" that sits a bit higher than 4 million and possibly undertracked by not much.
EDIT: Did not notice Gran Turismo.
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