StartrekCaptain,
I agree that the show Enterprise is inconsistant to known Trek Facts... but TNG is as well and is several of the TOS episodes.... however, you stated a quote from DS 9 in your first posting where they called the NCC-1701 the original enterprise, however, if you look closely at the case in Captain Piccard's ready room in the movie "Generations" the first Enterprise was indeed the NX-01 Enterprise, however it is not the one we see in the show.. it is a Deadelus Class Spaceship.. the flying sphere with a handle and warp nacells added.... that was Film Canon for the "First" Enterprise...
Second inconsistancy with the episode you quoted is that the First Captain of the NCC-1701 is unknown(Name not given in any TOS episode, however Captain Pike in the episode "The Cage" made it clear that he took the ship over from a previous captain).. Non-Canon sources call Robert April the first captain of the NCC-1701 (though still unconfirmed according to film), followed by Captain Christopher Pike (The Cage, The Menagerie), then Captain James T. Kirk... Kirk was the Third Captain, then Captain Spock (Star Trek II : TWOK), but the most notable of all her (NCC-1701) captains was James Kirk...
Third inconsistancy is calling the NCC-1701 a "Constitution Class" Starship, when in fact in any TOS episode, the dedication plaque next to the turbo-lift clearly states that the NCC-1701 Enterprise was a "Starship Class" Spaceship and is stated as such in "The Cage".. and was further made proof when Gene Roddenberry stated that Franz's (who called it Constitution Class) book on Trek ships were not Canon, and only what is seen on screen is Canon, and if any inconsistancies exist in furture episodes, the first showing of Said Canon is the one that is True Canon... the rest are just from writers who can't research.
However, you are correct, the show Enterprise is not Canon by Roddenberry's definition as the NX-01 was already seen on screen as a model in a historical case on the NCC-1701-D... as well as technonogy, equipment, weapons, ETC...
The way to determine Canon in Trek is to watch Trek episode by Episode according to production date... Starting from "The Cage" TOS first piolot episode all the way through until present day... Everything seen as a First that doesn't contradict a previous episode is "Canon" as per Roddenberry.
In response to another poster... Lasers were the top of the line hand held weapons in "The Cage" as Phasers were ship mounted weapons, or a huge cannon that could be transported to the surface of a planet... Hand held Phasers only became available between the time after "The Cage" and when Kirk took over the Enterprise... Phase Pistols leads to incline viewers of "Phasers". A shortened name of Phase Pistols would be Phasers.. thus, looking at this point of view, makes Phase Pistols an item out of it's created timeline according to TOS episodes... the Lasers in TOS were also called Laser Pistols.... Lasers for short, just like Phasers are short for Phaser Pistols...
Like I said above, if you want to follow Canon, watch each episode according to production date (not release date) and follow Roddenberry's rule I stated above.. this will give you True Canon of Trek.... instead of speculation...