As said we would do a slow change to allow people to adapt.
Even if people adapt, old literature won't. You have a century and a half worth of astronomic articles and books using the "old" system. Anybody that needs to extract info from this literature would likely run into the "old" stellar classification system and would need to learn how it works - which in the end makes a new system pointless to begin with.
Also, a lot of people would likely hold onto the old system for a long time. So you'd have a messy mix of literature using both the old and the new system. What's worse, a lot of the letters of the alphabet would be used in both systems - escalating the confusion even more, since you might not be sure what system the author is using. So, this article says that RandomStarX is a class B star - does that mean that it's a blue main sequence star, or a brown dwarf?
You could also just edit all the old books and whatnot to use the new system over time.
Just edit all the old books? Do you really think it's that simple? There's no vault where every single astronomical book published since the 19th century is located and where they can just go and change over to the new system. This literature is scattered everywhere, and a lot of it likely isn't even on the internet.
I can say this almost for sure because, as a palaeontology enthusiast, I have the misfortune of constantly seeing this. Just one of many examples - even though the ICS produced a "logical" stratigraphic system for the Ordovician some time ago, which had little in common with most previously used systems(e.g. the North American and Welsh, which to my knowledge had only minor flaws), few use it, sticking to the old systems. And nobody is updating the old literature, that I can guarantee. So now you have an even bigger jumble of systems.