As you well know the topic at hand is people using that data to "stalk/harass/intimidate" as the OP said verbatim. Which is not protected by the 1st amendment.
I read it differently; "this stunt" is ambiguous in context.
In any case, I think you're misunderstanding the nature of the problem. The danger of "doxxing" is that people get overwhelmed by a flood of negative attention from many different people. In most cases, none of the "harassing" individuals actually do enough individual harassment to make the action illegal. You can't go after the doxxer because releasing the information was completely legal, and you can't go after the mob because none of the individuals have done enough to constitute a crime.
You could certainly go after a guy who sends a knife; pretty sure just mailing a knife is illegal in most places.
I think you're misreading this. Doxxing is the online equivalent of incitement to riot; as in a real riot, the chances of any individual participant doing anything blatantly illegal are low, it's the cover that the crowd provides for lawless activity and the intimidatory factor that's problematic. So if you're unpopular with some group in your town, and someone says 'Let's go to Byerley's house at 123 Quiet Street and make some noise' that could count as incitement to riot even if your name and address are widely available.
The problem is not the mere repetition of publicly available information, but its strategic use to focus the anger of a crowd upon a relatively defenseless individual. That creates a dangerous power asymmetry with the explicit or implicit function of intimidation. It's not a big deal if people peacefully protest in front of the White House - the President and his family live there but there's a bunch of secret service people to keep him safe due to the nature of the office, same way there are police permanently stationed outside the official residence of the UK prime minister. If you're Joe or Jill Ordinary and a large crowd shows up on your physical doorstep, you have a serious problem.
Virtual harassment is not immediately threatening in the same way but it depends on how far it goes. If I write something controversial and make it public and get a storm of hate email in my inbox, that's annoying but not really worrying. But if I start also getting telephone calls or snail mail (or seeing such things quoted in emails) then it's quite a bit more worrying.
There's a limit to which people can control the amount of their personal data that becomes public. For example, I own a house which means I have to pay property taxes, and where I live property ownership is a matter of public record. So I was surprised after buying the home to suddenly receive a huge amount of junk mail from companies who obviously subscribe to lists of property tax payers. I can't take back that information. Should everyone be expected to set up a shell company in order to purchase real property and still maintain some privacy?
The best hack to get around this is to create a holding company, so then that holding company name appears instead. This might be a costly measure, but well worth it if you value your privacy. However, in most property records also include an address to where the yearly property tax bill is sent, so you might also want to set up a PO box.
As I said, 'Should everyone be expected to set up a shell company in order to purchase real property and still maintain some privacy?'
Personally, I prefer the European approach of the Data Protection Act that gives consumers a fair bit of legal leverage over how their personal information can be used commercially, as opposed to requiring people to engage in expensive obfuscatory security measures.
What does constitute enough harassment in your opinion?
You make it sound as though there's nothing to be done against this. But that is not the case, things change. Perhaps releasing personal information about another relating to doxing should be made illegal. It's not as if it's hard to distinguish between someone who's trying to dox another and legitimate sharing of information.