the original enterprise was designed 50 years ago, I don't see the need for the the enterprise in Discovery to identical to any of the designs made in the 60's. That said, it's not that different at all. It still has red buzzard collectors, albeit they are lit up now, still has the satellite dish deflector, doesnt appear to have any added joints or pods or anything like that.
The nacelles are different. The nacelle struts are different. The shape of the secondary hull is different, particularly at the back where the shuttle deck is. The impulse engines are different. The colour and hull detailing is different. But yeah, apart from all that it's not
that different at all...
I'm going to go slightly off-topic here, so apologies in advance. But I think Discovery is having a similar-but-maybe-reversed problem to the one that Enterprise as a series had. Enterprise sort-of failed because they fell into the trap of not wanting to change too much despite going back 100+ years pre-TOS. Some things could have been really interesting - the ship doesn't have shields, or a tractor beam, the transporter is a comparatively recent invention. But they ended up with polarised hull plating that does the same job as shields (right down to the "...down to 25% captain!" trope), a grappler that does the same job as a tractor beam and almost equally as well, a transporter that beams people around faster than the one on Kirk's ship 110 years later. The ship is supposed to be much slower than later ones, but it still gets to a different planet each week. Phase cannons act just like phasers, photonic torpedoes exactly the same as the torpedoes later in the Trek timeline.
Discovery now
wants to change stuff. They want to show a different method of getting around the galaxy, want to show things that we haven't seen before. But then they've set it right smack in the middle of an era that we
have seen before. So none of this cool new stuff fits. There was absolutely no need to bring the Enterprise into the show. None. Just like there was no need for Sarek to show up, or Burnham to have been adopted by him in her backstory, or any need for Mudd to show up. It just smacks of the showrunners being desperate to shoehorn this show into canon but not wanting to compromise Their Vision For The Show™ with bothersome continuity. So fine. You want to make your vision of Trek? Do a reboot. Better yet, set it
after the shows and films, right into uncharted territory. Show something new, not a retread over old ground and established events.