But would that have been realistic? I mean, the NX serves 100-110 years before the Constitution class enterprise (though we don't know how old that class is by the time TOS plays). It'd be like having a navy ship from the Titanic era have a refit to be more like the very newest Zumwalt destroyer class ....unless we assume technological progress between 2150 and 2250 was a lot slower than in the 20th century.
Technically the warp 5 engine is also supposed to leak delta rays, which should be a sufficient enough reason to replace the engine.
Small arms without a stun setting makes sense if the early Federation was more militaristic than anyone in later centuries would care to admit – to the point that a Prime Directive became an absolute necessity to have. It’s also possible that there were small arms dedicated solely with a stun setting to make up for that change, and officers carried both on a utility belt. It wasn’t like anyone was being vaporized with the phase pistols in ENT anyways. Changes were bound to happen, resulting in them starting over with TOS-y small arms with pulse phases. Projectile weapons make no sense, unless your talking about DY-class colonization ships that left Earth in the early 22nd century.
They had spatial torpedoes before the Xindi crisis, and they could have had them again in the aftermath or the Romulan War, due to the whole primitive atomic weapons deal, and a possibility of trying out a photonic spatial torpedo – shaped like a spatial torpedo, but the size of a photonic one. And the Romulan BoPs in the 23rd century were carrying atomic weaponry of their own, so there’s no reason to think that, up to the start of the Federation-Klingon Cold War at least, Federation ships weren’t doing the same thing.
It’s possible that the early transporters had a very limited lifespan, like a refrigerator or a computer, resulting in numerous transporter accidents. So, no one wants to use them anymore (or they’re even banned for a time), resulting in their removal until the technology has been perfected – which would be the TOS transporters. Until then, a reliance on shuttles & aqua-shuttles (TAS) would be needed for away missions. And restocking of supplies would necessitate stops at starbases, instead of just beaming those supplies from a passing cargo ship, since all supplies would have to be manually brought on board. And when reintroduced into service, transporters could have been much smaller, and been relegated to cargo only before being expanded to transport officers, and then civilians.
Robotic arms make the most sense to succeed the grappler, if the early Federation had not yet figured out tractor beam technology.
The various scanners (hand scanner, medical scanners, heavy scanner) are technically primitive tricorders, that were made to be practical for use on a ship with limited space onboard. The terminology just hasn’t entered use yet. And the tricorder in ST’ 09 onboard the USS Kelvin resembles a briefcase.
Stealth against sensors & electronic warfare would be useful in an Earth-Romulan War setting, as well as a Federation-Romulan Cold War, Federation vs Klingon Cold War, Section 31 missions, and a conflict with the Sheliak.
And we know about holographic technology on the bridge. And the Constitution class vessels are supposed to have recreation rooms, so a small recreation room could have been installed at some point as well.
We are assuming that the NX-class got retired permanently, instead of the possibility that they were taken out of mothballs and reassigned for other missions related to Section 31. There is a clear Section 31 influence by the time of DSC; there is no reason to think that the reassignments of the NX-class ships weren't the beginning of that. Circa 2156 – if that was when the refit happens - frequent transporter malfunctions to the point of its removal, robotic arms, stealth against sensors, and electronic warfare likely exist. Everything else happened after the founding of the Federation.