Honestly there's far more mounts that by the same logic would be '' immersion breaking ''.
Outside of the story I have a hard time being immersed in MMO's to begin with because of the mere existence of other players.
Both in how many they are and also what they're doing and how they behave, unless maybe you play on a RP server where everyone takes it really seriously.
There sure are a lot of WoL's running around...
It's the same in WoW too I have a hard time to really feel like '' the Champion '' because there's a billion of us.

Like I sorta got into before, what happens in the story is one thing and should be consistent ( there is still modern clothing tho... ).
But outside of that you gotta give players some room to have fun.
Not everything in the game is always meant to be '' canon '' at all times, that's why we literally have cars in the game...