Close
As someone who is not familiar with áll the Fate stuff I've found it really a mess to deal with.
Even as someone very familiar with Fate, the class tags don't make much sense these days for exactly the reasons you describe. For many years there was only one or two servants we knew in each class, but now there's at least a dozen or more. It's especially bad for characters with multiple classes like Elizabeth Bathory and there's more of those coming all the time. I think it makes much more sense to just go with the character name. With the original Fate/Stay Night game you didn't find out their true names until late in the story so I suspect class tags were originally chosen to prevent spoilers, but that's just confusing now and Type Moon aren't really making any attempt to hide the character's true names any more.