Bureaucrats wouldn't allow for it being impossible to tell apart the Constellation from the Constellation!
Tell us something we don't know! If the original Constellation
was a starship of the 10th (and therefore older) design, chances are high that the ship was lost in action, decommissioned, donated to the Starfleet museum or whatever.
Chances are high that by the time Matt Decker's Constellation
is on active duty (16th or 17th design?) the original one no longer is.
You are finally the second (as far as I've been able to learn) who understands the essential, philosophical and ethical purpose of the debate!
My viewpoint is clear: Not to acknowledge he original intentions of the creators would be an act of ingratitude and disrespect, to acknowledge the retcon revisions of the subsequent producers would be like rewarding them for bad behaviour (i.e. inaccurate and lackluster research).
The worst offender here is undoubtedly the bridge plaque of the USS Defiant
in "In a Mirror, Darkly". The producers knew
that it said "Starship Class" on the original bridge plaque in "The Tholian Web" (in a manner of reading "... Enterprise Starship Class"). To have that altered into "Constitution Class" was clearly an act of arrogance and disrespect at the expense of the original producers.