I hereby give you complete authorization to access over a network (but not physically) any computer I own. Nothing you do is unauthorized or exceeds authorization in terms of the CFAA.
The solution fixing the "Computer Fraud and Abuse Act" is not to amend it but to get rid of it. The Internet is world-wide, 95% of hackers trying to break into your computers are beyond the reach of U.S. law. Rather than providing a meaningful deterrent to bad hackers, what the law really does is create a chilling effect for our own creative geniuses. Genius geeks from Steve Jobs to Aaron Swartz should feel free to push the boundaries of technology without prosecutors and juries second guessing them.
Getting rid of the CFAA doesn't actually expose you to additional danger, which I demonstrate in the statement above. My computers are secure, which means that while I've given you legal access in terms of the CFAA to hack my computers, I haven't given you real access by giving you a password or username. I don't need the CFAA to protect my computers, I can protect them just fine myself. Or, if I can't, I've only made the threat 5% worse giving US citizens permission alongside all the hackers from Russia, China, Brazil, and so on.
Getting rid of the CFAA doesn't get rid of other crimes. While I've give you permission to access my computers, I haven't given you access to my bank account or credit card number. Neither have I given you permission to physically steal the computer. This means all those hackers who are now behind bars for stealing money would still be behind bars.