I think that's overstated.
First of all, it was the Magna Carta which established that the king was not above the law, so in that sense the founding of the United States was more "and we don't need a king".
Second, there are frequently legal discussions in the present day as to whether a sitting president can be charged with a crime, so there is at least a substantial idea that there is some "sovereign immunity" (quotes because that's not what sovereign immunity refers to)
Third, the founders were also well aware of the threat of political motives for prosecutions and wanted to diminish them with various balance of power checks and balances.
That is similar to the immunity given to the sitting US President. What is different is that monarch is not really expected to obey the law either. For example, the Prime Minister was fined for illegally not wearing a seatbelt. If the king didn’t wear a seatbelt, it would not be a big deal - the royal family freely ignore traffic laws (and more serious laws) without consequences. Queen Elizabeth did agree to start paying taxes, but there was never any suggestion that she be compelled to pay taxes, merely that it would be the right thing to do.
The thing about Britain's constitutional arrangements is that there are many things which 'can't' be done, which it turns out simply 'aren't' done.
There are also all the laws the monarch / monarch’s lawyers interfered with e.g. police can’t enter Sandringham Estate without an invite, leaseholders on the Duchy of Cornwall are excluded from buying their freehold
What is sovereign immunity?
Sovereign immunity is a centuries-old doctrine dictating that the monarch cannot be prosecuted or subject to civil legal action under the law. Its origin lies in doctrine and convention, rather than statute, and there is no law setting out the rules underpinning the concept.
It stems partly from the medieval concept that the monarch is the source of justice, and can therefore do no wrong. It also relies on an argument that because the courts belong to the Queen she cannot be compelled to appear in them, since she would, in effect, be prosecuting herself.
Since at least 1800, the monarch has also had a legally distinct private persona, created to allow them to have independent wealth and property that could be inherited by their children. However, the lines between the two are somewhat blurred, and sovereign immunity has typically been interpreted to apply to both the public and private identities of the monarch.
We take it for granted now, but it was a beginning of constitutional order - king and government should follow certain laws and rules for how to run the country. And the UK is after all a constitutional monarchy, no longer at mercy to the whims of an autocratic monarch.
The social/civil consequences of this sort of criminal indictment before election is enough to kill a presidential campaign and has enough times in history. As it should be.
This is behaviour before/after presidency when the stakes are far lower.
This just plays to Trump's strength as the ultimate rebel.
In terms of game theory, this is a very different game than Nixon or Bush. Trump annihilated the Bush Legacy, and is hated by both sides of the establishment.
That juice is not worth the squeeze.
It is so tragic and disappointing.
In Germany for example we have sort of an "updated" version, with lessons learned. But one thing I actually want changed is that members of parliament have actual real immunity. Not in the practical sense - immunity for individual members has historically always been waived by parliament at the slightest whiff of an investigation. But the example of Trump teaches us that it is a fallacy to trust in the decency of politicians and unwritten rules.
