A larger die would be needed, with the potential wide dispersion of ability scores. With a d20, if a person had really high mental stats and low physical, they'd almost be guaranteed to succeed no matter what, whereas the lower mental scores player is in more danger of failing if he doesn't roll high. Conversely, with a higher DC, there's risk of failure for the high mental player, but the low mental player is almost guaranteed to fail.
If you made it a modified Wisdom check or something, a d20 would be better. But adding 3 scores together like that, you'd almost definitely need a d100, or some other clever mechanic.
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