No. The job of the government is to use patents "to promote the progress of science and useful arts." Says so right in the owner's manual. Patent trolls are exploiting legal loopholes to do the opposite of "promoting progress," so the laws need to be adjusted to fix this. As far as I'm aware, private entities cannot pass laws. So. The government needs to be involved. And they need to do a better job.
I think we'll just have to disagree. It is my opinion that answers of the form, "well the only problem is that the laws are just a little off and it can all be fixed with a few tweaks," are incredibly naive. They've been repeated over and over as government has grown in size. It ignores the fundamental problem: at the end of the day, it's just humans making and enforcing the laws, and they are under extreme pressure by the system to become corrupt and bend the laws in their favor.
If you want a system of IP run by elected representatives, then you've got to accept the corruption that comes with it.