The problem of this design is the secondary hull. The actual NX is closer to the rocket design of the Phoenix and the NX prototypes and thus emphasized design history better than a ship which would have already featured a secondary hull. Furthermore the single biggest mistake of the show was that it wasn't rooted deeply enough in the 22nd century. A ship which looks like a 23rd century design would not have alleviated this problem.
I liked the design of the NX, though I didn't care for it as a stepping stone towards the eventual TOS Enterprise. It felt out of place and too advanced. Had the show been better overall, I would have likely overlooked the design of the ship, as I have with the design of the Abrams Enterprise, but as Enterprise suffered across the board, the ship is just another problem to throw on the pile.
I don't buy the NX-01 looking "too advanced" - TOS was made in the 60's, and it shows. If the Gorn from "Arena" is really a fearsome lizard monster when it's obviously a guy in a bad rubber suit, than the original Enterprise is an advanced futuristic starship, whether it looks as it did in 1966 or the 2009 movie.
In a Mirror Darkly showed that in-universe-wise the sleek Constitution looks more modern than the "guts-sticking-out" NX.
I would have preferred a design similar to the Conestoga, something closer to the Phoenix's "rocket between two nacelles" look. No bridge on top, though. Put it at the front of the ship.
IAMD is great in that it canonically disproves the fan complaint that the NX is too advanced for a TOS prequel. The prime universe Connie stomped all over everything in the mirror universe. Considering that the mirror NX was likely more advanced than the prime NX due to the nature of MU starfleet it goes to show just how lightyears ahead TOS tech is compared to ENT tech.
I don't care for the version whose sketch is posted above, especially the secondary hull, which looks 'awkward' to me.... I had never seen John Eave's 'second' NX proposal (thank you for including the link!), but I think it is a really nice design. But if the NX we got is the 'Akiraprise', then that second Eave's design would have been the 'Galactiprise' with those retractable nacelles coming out from the sides. I would have liked to have seen the 'Galactiprise' on screen as another early Earth vessel, but still prefer the NX-01 that TPTB gave us.
By some arguments, the NX is close to a future SF design, the Akira. It's not a bad thing to see certain design ideas reused either way. ^ This one has the proportions of an Ambassador class with some of the lines of a Sovereign class. Nice looking ship, but I'm OK with the NX being what it was.
The obsessive "Akiraprise" complainers appear to have all moved on to this beauty: "It's too big!" "The nacelles look like penises!" "The engine room's a beer brewery!" "lens flares!" "Apple store!" Poor old NX-01's been forgotten
Ah, true. The only thing I don't like about the JJprise is that the aft hull undercut is too far forward. The neck too. MAkes it look like the entire engineering hull needs to be slid backwards.
Move the neck and saucer forward and space the nacelles out a little more and they would've had a winner.
^I like it because it has a TMP vibe. Of course what do I know, I barely remember which ship is what.