The president of the USA has the equivalent of the Royal Prerogative and, I am reliably informed, used it to set free those who tried to overthrow democracy on J6. He cannot, however, appoint bishops.
The current SCOTUS wants to extend this power by making presidential executive orders to be the law under the unitary executive/ presidency theory. In both the US and UK, the prerogative is currently subject to the courts as Boris discovered when the Supreme Court found his proroguing of parliament to be illegal.
Thus it cannot be said that the UK prime minister has excessive power. Much more worrying is the pernicious ‘influence’ of the royals. Charlie has twice used this to negate planning permissions already given: the national gallery and Chelsea barracks.
The Homeopathic hospital within the NHS is, thanks to Charlie, not subject to NICE and he has had some success in holding back genetic engineering as that is “god’s work.”
Of course, Charlie is immune from prosecution and SCOTUS has granted the same to POTUS.
But no-one is above the law, ha ha.