by bwingrave
I think of it as a feature that allows you to do useful things even if you don't have a card of the role you want.Consider the following:
If there was no option to petition, if you wanted to lead or follow the Patron role, and if there was no Patron card in your hand, you would need to play a Jack to do so (if you had one). So if you didn't have a Jack or a Patron card, you wouldn't be able to lead or follow Patron.
With the petition, you have a third option: discard 3 cards of the same color to lead or follow any role. So if you have three Laborer cards, you can still lead or follow Patron by petitioning.
Petitioning tends to reward people for building up bigger hands, since they're more likely to have 3 cards of the same color in a bigger hand.