No, not at all. I just think the term is so subjective that it can legitimately be used by one person on an item that to another person it would not fit.
To me the Anson & Deeley action is a 'classic' in that it was a real design innovation that changed the market and has endured. Matters not who made it.
The Westley 'drop-lock is a 'classic'. But is the Field 'Gun of the Future'? That is also old, but was failure can it be a 'classic' on the fact it is old or dismissed because it was failure?
For guns, I'd reserve the term in my own usage to guns and models that were typical of type and successful in their time:
Beesley 1880 self opener
Grant & Hodges side-lever HG
Holland 'Royal'
Baker 'Climax'
WR 'Droplock'
Greener Facile Princeps,
etc
A hard one to make a real axe for though.