Gene Vincent - yes
Beatles - yes
Byrds - yes
Black Sabbath - no
Eagles - certainly some of their earlier stuff
Blasters - yes
Police - no
"Traditional rock?"
Well - the Byrds were not considered a traditional "rock" band at all in the 60's; they were the ones who started the "folk rock" genre. It was a new thing. Black Sabbath is more of a traditional rock band than the Byrds were - but your categorization seems to place, by reference, "metal" outside traditional rock....but folk or country rock in?
The Eagles - especially their earlier stuff - were more of a country band than today's country bands, and were the (In many player's opinions) a kind of watered-down result of blending Gram Parson's vision with commercial music. And what makes the Blasters - a rockabilly band - more "tradional rock" than the Police, a...well, "rock" band?
Where do you put Led Zeppelin? Yes? Cream? The Surfaris? Was Cream traditional rock...or blues rock...or jazz rock...
Frank Zappa?
...or what the heck does it matter?
I use labels as well out of convenience - because generally it helps people understand what you mean.
That list I do not understand at all.
Heck, as long as you have a gig, who cares what people call it? If you don't, either you're hanging around the wrong musicians or hanging onto stuff YOU want to hear - but the public doesn't.
Complaining about traditions and not being able to hold onto them isn't applicable to commercial music. The commercial world could give a damn about anyone's traditions - they care about what sells, and if calling Rascal Flatts a "country" band somehow translates into ticket sales - then they ARE a country band.
Marketing only does so much. Eventually the music AND entertainment (because the stage part of it IS just as critical when it comes to sales) stand up or they don't.