The top marginal rate in the UK is approximately 60%. Any American who renounces their US citizenship for tax reasons is mathematically challenged.
You are missing the point, becoming a British citizen doesn’t make you liable for British taxes. You only pay UK tax if you are actually resident in the UK, whether you are British or foreign. Whereas US citizens pay tax no matter where they are.
I am a UK citizen living overseas and I haven’t paid tax to the British in almost eight years. I have a good friend who hasn’t lived in the US or earned a penny in the US for the same length of time and he was called to the US embassy where his passport was confiscated and he was told he would not get it back until he paid tax outstanding on income he’d earned overseas but which the US tax authorities wanted.
He’d never received an iota of assistance from the US government but here they were tracking him down to SE Asia to get him to pay tax.
Many American people have a rather naive view about how “free” they are in comparison to other nations. I wouldn’t like to be a US citizen, it confers no benefits that many other nations don’t equally confer but without a lot of the hassle.