Can they claim a tax credit for supporting that bandwidth usage and handling abuse?
At best, it's a burden for no solid gain for society. At worst, there will be loopholes used to DoS businesses because they can't shut down individuals due to law-given rights, and that will lead to court fights.
These rights would do nothing but save scraper authors from learning to obfuscate their actions.
If one makes information "public" but don't really want to share it, then the public is fully justified in taking it.
That's why you routinely publish your bank account, social insurance, and credit card details online, right?