(the UK hasn’t got free speech as an enshrined right)
In practice, does the US?
Categories of speech that are given lesser or no protection by the First Amendment (and therefore may be restricted) include obscenity, fraud, child pornography, speech integral to illegal conduct, speech that incites imminent lawless action, speech that violates intellectual property law, true threats, false statements of fact, and commercial speech such as advertising. Defamation that causes harm to reputation is a tort and also a category which is not protected as free speech.
https://en.wikipedia.org/wiki/United_States_free_speech_exceptions
It seems to me there are a lot of exceptions to free speech in the land of free speech. I wouldn't see any harm in adding hate speech to the list given how large it already is.
e.g. passing a nearly-identical law copying Thailand about the royal family and putting in prison anyone who calls Prince Andrew a pedophile.
That seems more of a problem with flawed democracy or autocracies, than to do with free speech. Any awful thing could become law under a flawed democracy/autocracy. The UK has plenty of undemocratic elements and they're abused to pass horrible laws right now, and we need to fix those elements - the laws are just the end result.
With this context, it gets more interesting:
Well, it doesn't seem to have worked – at least not in the short term. So now they can't have sex and they're not marrying either, worst of both worlds. Maybe they also wouldn't have a prison overcrowding problem if they stopped jailing people for things like these.