The idea is that when you have tab bar full of Showdown servers, you could easily recognize that for example Frost is Frost. You don't care if they use Pokemon Showdown as their client software, as they all use the same software. When all servers use the same favicon and title, the tab bar looks like this. Clearly useless, right?
View attachment 37918
(this example is ridiculous, I know, but even with two different servers it's annoying)
As for not realizing it's a Showdown server... well, if you visited a website, you should know what it is. Besides, if you visit Frost, you want to know it's "Frost", and not just "Showdown". Similarly, in bookmarks, "Showdown" is non-descriptive (although the user can provide his own title for bookmark, why make him do that, when it's completely unnecessary if websites would be allowed to have their own titles). If you view the tab you opened, there is a clear hint this is a Showdown server, that is, "Pokémon Showdown" of a page (also "Credits" button saying it's Showdown server).