Then again, by WWII the UK was demilitarising. Australia knew full well the Royal Navy could not fight a war in Europe and the Pacific even though they maintained the fiction of the 'Singapore Strategy' to the electorate.
cam Freedom, Liberty, Equity and an Australian Republic
I think that the difference between the US and Britain in this respect is that British imperialism and British elites were tired, so they lacked the will to fight the desire of the people. Americans today want an empire no more than the British people did at the end of WW II. The problem is that American elites still think that empire is a going proposition for them, so they are not willing to give the American people what they want.
I think Johnson has a simplistic notion of how nations choose the paths they take. He writes as if nations can choose which way they go, the way a person can plan out their career. It isn't like that. Nations have destinies, determined by institutional, cultural, and other constraints, over which they have little control.
Which is not to say that I have not been impressed by his argument that empire and democracy/republic are incompatible, and accepted it.
On the other hand, Britain managed to be both a highly successful de facto republic and a highly successful empire for over two centuries. So Johnson's thesis isn't a useful practical (or theoretical) guide, although it is a very good talking point, which is perhaps all he intended it to be. A bomb, H bomb, Minuteman / The names get more attractive / The decisions are made by NATO / The press call it British opinion -- The Three Johns
There was nominal democracy much earlier. But even though the franchise had been widened to include almost everyone by the end of the 19th century, it wasn't until the Labour Party started gaining significant interest that the working classes had real representation in parliament.
Political forms are much less important than whether the system as a whole is driven by the elites for their own benefit, or by the working classes.
Oligarchy is the natural backbone of empires, but sometimes it puts on democratic clothing and tries hard to look innocent.
I think his point his, once you get to that point you have two choices, either democratise and cease to strive for empire, or become a dictatorship and try to hang on to it by sucking any remaining worth out of the country. His example for going the latter way was Augustus Caesar.
There was a time when Britain's economy was like the current American one. It was way ahead of all its rivals in size, ability to attract capital, technology, output, productivity etc. After WWII that mantle had moved to the US.
The other aspect is that British Empire was built on the Royal Navy. At the end of WWII empire came through airpower, and naval projection was dominated by the aircraft carrier. In 1945 the US was pumping out something like five aircraft carriers a month in production. Britain couldn't compete in the expense department. Yet a century and a half earlier when expensive copper plating was a technological jump, Britain plated their ships as quickly as they could.
I think you are correct that the elites get to make the decisions relating to empire and whether it continues or not. By your definition, increasing democratic input into the political process suggests empire becomes harder and harder to implement with public opinion as the people rarely want it.