Well, it was WW1 and it was an active actual danger. Not perhaps as in removing the monarchy but that it may sap morale. Hence a lot of people in power and business made the change.
I hardly see why it’s a relevant thing to mention today, though. It’s not just you, I have encountered many UK republicans who seem to have this be the very first thing out of their mouths when the topic of the monarchy comes up.
Because Rule of Cool. A republic has its many advantages, but will never be as cool as a monarchy, nor as an empire. And a globe-spanning empire is the coolest thing ever!
Empires are only cool to people who don’t live in them. All the evidence suggests that, by and large, the people who do live in them can’t get out fast enough!