This feature serves no real democratic purpose. It convinces people that they can influence policy with clicks of a mouse, yet when they find that their petitions go ignored, they will only become more frustrated. American Government should not be flippantly regarded, as though it were a reality show.
If Americans want to effect real change, they should get involved in politics. Run for office, campaign, form a lobby or otherwise functionally engage the political process.
A secondary reason for dissolving this feature: Media sources use the more extreme or absurd petitions as "news" stories designed to stir up negativity and strife. Most readily to mind are the petitions for "secession" - but most recently one to deport a journalist for stating an opinion.