Gate-check will remain free. No way they start charging for it; there are too many logistical and other issues to deal with. And, yes, people will now carry-on more, leading to longer lines at the TSA checkpoints and more chaos on boarding as there will be less space in the overheads. It is going to suck, even for folks who normally wouldn't be checking luggage anyways.

Ironically this policy may lead towards elites/FFers checking bags since it will be free for them and they'll not want to fight for overhead space. I won't go that route but some might.