Does anyone have a practical defence of why the PM standing down shouldn't trigger an election, other than 'thats the way it is in a Parliamentary Democracy' or 'who else does that'?
Yes, I'll have a bash.
All of the World's liberal democracies are built upon a fundamental principal: those who make the law ( the Legislature) are separated from those who implement and manage the laws (The Executive), and that both of those groups are separate from those who judge upon transgressors of the law, (The Judiciary). It is commonly referred to as the separation of powers. In the UK the Parliamentary system that underpins our democracy manages this separation in an incomplete manner. That is to say that the separation of the three powers is not absolute. At the very least they comes together under the Crown. However, only a part of one of those bodies is elected into power by the people. That is for membership of the House of Commons - the senior body of the three bodies comprising the Legislature; the other two being the House of Lords and the Monarch. The Commons is the senior body because it controls the purse strings. Both the Prime Minister (as First Lord of The Treasury) and the Chancellor of The Exchequer (his No. 2 in the Treasury) must be drawn from the House of Commons.
And this is where the imperfections in the separation of powers come into play. Members of The Executive are NOT elected into their posts, they are appointed. Firstly, the Prime Minister is appointed by the Monarch, then the remainder of the Executive (ie The Government) is appointed by the PM. However, whilst members of the Government are not elected into their posts, they must be serving members of Parliament: ie. members of the Legislature. This means that as members of the Legislature every member of the Executive counts just as much as the greenest, newest backbencher. Liz Truss only has one vote as a law-maker, just the same as every other MP.
Formally then, there is no reason to have an election because members of the Executive are changed every now and again.. We all know that membership of the Cabinet is in the gift of the Prime Minister. We do not have an election simply because the PM chooses to boot out the Home Secretary and replace them with someone else. Likewise, because the Monarch changes the Prime Minister - provided that the new candidate has the support of the majority of members of the House of Commons - then there is no need for an election. And there lies the key to the individual who becomes PM. They must have the support of the majority of the members of the House of Commons. If that cannot be secured then before an election is called, the Monarch will ask the Leader of the Opposition if they can secure sufficient support to form a Government. If they can (usually because a critical number of MPs from the Party in power have crossed the floor of the House), then they will do so. However, it would more than likely that the new PM would have to call an election because governing would be practically impossible.
As for the Judiciary, it used to be the case that whilst it is separate from Parliament, the senior judges were appointed by the Lord Chancellor, a Government Minister. Since 2006, this has been changed so that an independent commission chooses the best candidates and then puts them to the Lord Chancellor for installation.