Grantanow
You make some valid points, volver, but the difference between an Elected Head of State and a constitutional Head of Government is not quite as clear cut as you imply. The example you give of the German EHofS to counter my examples of France, etc., is a case in point: the German President holds considerable reserve powers going well beyond what our constitutional monarch can do. For example, in modern times the President has refused on nine occasions to sign Bills passed by the Bundestag (the last time that happened in the UK was in Queen Anne's reign when she refused one Bill). He can of his own discretion dismiss the Chancellor, dissolve the Bundestag, declares a state of emergency and grant pardons amongst other things. One other point about the election of the German President by the specially convened Convention is that he is almost sure to be a member of the majority party in the ruling coalition which to my mind is a political risk in an EHofS.
That's interesting Grantanow, thank you for posting about the German system. Presumably they have decided that is the system that they want. I don't think there is anything inherently wrong with a Head of State declining to sign a Bill. Our House of Lords often send a bill back for the Commons to look at it again and most of the time we just accept that as normal.
There is no need for us to adopt that model, or to have a President elected by a political Convention. We could all have a vote. Although of course, some think we're not really capable of deciding such a thing and might get it wrong. 😉
I'd reform the House of Lords too, but that's another thread 🤣