Cheaper, easier parking -> more demand for driving -> more traffic -> hard to find parking again. Plus the additional traffic.
A better solution would be to encourage the use of non-automobile transport through increased public transit investment (more service). That would free up plenty of parking for those who still choose to (or must) drive. Or to encourage ride or car-sharing, thus maximizing the effectiveness of existing parking (more people served per parked car). Also, raising the price of parking on-street would make more parking available, both by discouraging some existing parking and making off-street lots more profitable for operators.