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"First, much better to say 'we' instead of British, we then know that the question has been asked by a fellow countryman."
Would it matter if it wasn't? This seems largely semantic.
"We are easily persuaded to ban something if that something is a popular request. Obviously if it was not popular it stands to reason, we would not be easy to persuade."
I get what you're saying, but I'm not sure it's true. People don't usually seem to endorse bans based on whether they're popular or not - they usually see them as a means to some end.
For instance, "We should ban smoking in pubs to protect ourselves from second-hand smoke"
or
"We should ban fox hunting because it's cruel."
I don't think you hear many people saying "We should ban x or y because it'll be popular" - purely because I think a lot of people accept the majority isn't always right, and unless there's been extensive polling, it can be hard to know if you're in the majority or not.
"Not quite sure what your observations are"
They're covered in more detail in the OP, but the heart of it is this: I think people have a very cavalier attitude toward banning things, my evidence (admittedly skimpy) being how often I hear people endorsing it as a solution to one problem or another (you see it on here a lot as well but you're likely to hear it if politics comes up in r/l too). Further, I think it's inconsistent with the expectations people have of the government.