The main advantage of it compared to the UK model is that the underlying main principles are clear and part of one document, where in the UK already all ot that is scattered across so many different documents.
The codified constitution is useful, or not, to the extent that it assists in resolving questions about the powers and duties of various branches of the state.
The problems we're having at the moment in the UK are caused by the applicability, or otherwise, of particular procedures in the highly unusual political circumstances in which we find ourselves.
The problem isn't that these procedures are particularly obscure -- there's no mystery about the Fixed Term Parliament Act, for example. The problem is that the government finds itself in a situation that hardly seemed possible back in 2011, when the Act was passed, and is trying to use it in circumstances no one would have dreamed of.
Similarly, it's no surprise to anyone that Parliament is prorogued -- suspended -- for much of September in most years. What's unusual is, again, the circumstances in which it is proroguing and the length of time for it's being prorogued.
The problem isn't that the provisions are obscure but that they're normally so mundane and automatic that no one ever stopped to think what would happen if some PM were to start to use them in the way Johnson has been doing.
Now I come to think of it, presumably Poland, Hungary, Italy and Turkey all have written constitutions, as, of course, does Ukraine (and I have in mind the problems going back before Russian military involvement).
They, however, haven't proved particularly effective in preventing the takeover of democratic systems by the authoritarian, populist right.
So it can't just be a question of having a written constitution.