Why would Parliament after so many reforms continue to support the monarchy?

Traditions are very difficult to eradicate. Even though modern people in countries like England might wonder why there is any need for a monarchy, it is still seen as a powerful symbol, and the British people have become accustomed to it. Thus, while Parliament actually wields the legislative authority, the Queen is seen as a reminder of England's long history. It is doubtful that Parliament would want to get rid of a symbol that many citizens still regard with affection. And even those who criticize the cost of maintaining the monarchy still tend to agree that the image of the monarch is one that unifies the nation.

Why get rid of what, to many British citizens, that which has become a fondly regarded institution to the British people. Take, for instance, the British Commonwealth of Nations, what glue would hold this group together if not the British Monarchy. No Parliament in its right mind would , dare I say it, even consider a referendum. Hence, like perpetual motion, from something the French have given us:-

"Le Roi et mort, vive le Roi..." or, in English...

"The King is dead, long live the King...!" ...in perpetuity...