What you offered up is in no way comparable to this:
Since 1900 Britain has had 22 different Prime Ministers. Our list below shows that in that period there have been 14 occasions on which 13 different Prime Ministers have come to power other than through a general election.
| Year | Prime Minister | Party |
| 2007 | Gordon Brown | Labour |
| 1990 | John Major | Conservative |
| 1976 | James Callaghan | Labour |
| 1963 | Sir Alec Douglas-Home | Conservative |
| 1957 | Harold Macmillan | Conservative |
| 1955 | Sir Anthony Eden | Conservative |
| 1940 | Winston Churchill | Conservative |
| 1937 | Neville Chamberlain | Conservative |
| 1935 | Stanley Baldwin | Conservative |
| 1923 | Stanley Baldwin | Conservative |
| 1916 | David Lloyd George | Liberal |
| 1908 | Herbert H. Asquith | Liberal |
| 1905 | Henry Campbell-Bannerman | Liberal |
| 1902 | Arthur Balfour | Conservative |
You can add Theresa May.
It’s rare because we vote for president and vice president at the same time. And we also don’t have the ability for Congress to decide with a simple majority that the current president is a douche and needs to go.
Sounds terrible doesnt it. Actually NO British prime minister comes to power through general elections. They are NOT elected, except as MP’s. However, by the same token it is very easy to get rid of them, very quickly, if they screw up or lose the confidence of the House of Commons. That makes for very fast transitions of power and therefore stability of government.