I think if we define 'cancel culture' as merely the "whiny complaint of people who previously could say anything they want, but who are butthurt that they don't get to say anything they want anymore", then it is indeed, merely a whiny complaint, and one which you've done a very thorough job of discounting.
But I think there is another phenomenon, which is what I think of when I think of 'cancel culture' (but which you can call whatever you like) that I think is worth more exploration.
And it's essentially this: as a culture, we've learned to cancel people for the wrong reasons.
Sure, people have a right to say whatever they want - and there are plenty of platforms for doing that nowadays. And other people have a right to direct their attention wherever they want - which could mean diverting it away from someone who says things they don't like.
People don't have to tolerate everything. There is a line that needs to be drawn for what we tolerate. But I think we are collectively drawing it in the wrong place.
Because, right now, the line we draw is this: does the person's current opinion match my current opinion? And if the answer is "no", then we consider that person evil and intolerable. Drawing the line of tolerance based on currently held opinions is bad. It degrades dialogue and the exchange of ideas.
Where we should instead draw the line is with manner and intent. If a person starts throwing accusations and insults, or is clearly trolling, and not receptive to dialogue, then that is a great time to divert our attention and 'cancel' them. But if a person demonstrates that they are speaking in good faith, and with an open mind to changing their point of view, we should not divert our attention, even if their opinion is different from ours.
That is what we need to make our society better. And when I see articles like this, I worry that it provides an excuse for continuing a culture of intolerance that is ultimately toxic and irresponsible.
I agree with you that America doesn't have a free speech problem. But we do have a good speech problem. and a good listening problem.