In my opinion, it's a totally reasonable request. It's not a reasonable expectation, but that is a different matter. I'm not sure what the 'purpose of the internet is' but I don't think Al Gore had such a request in mind when he invented the internet.
It is a reasonable request to ask your neighbor to take down their billboard that says "THE GUY NEXT DOOR WROTE ${THIS} BLOG POST AND IS A REAL PIECE OF SHIT", even though they aren't obligated to do so. It becomes unreasonable when you expect that they take it down.
FWIW, calling somebody a piece of shit goes against personal insult laws in many countries, so in your particular example, the neighbor may in fact be obligated to take down the billboard, or at least to modify it.
FWIW there are few expressions of free speech that aren't in violation of some arbitrary law enforced by some arbitrary country. It was probably short-sighted of me to assume that my exaggerated example wouldn't be recognized as hyperbole, but honestly what is the point of this comment?
Everything depends on jurisdiction, that's the very nature of law in and of itself.
It is a reasonable request to ask your neighbor to take down their billboard that says "THE GUY NEXT DOOR WROTE ${THIS} BLOG POST AND IS A REAL PIECE OF SHIT", even though they aren't obligated to do so. It becomes unreasonable when you expect that they take it down.