This is usually my reply: we've only seen a small handful of TOS-era ships (if we count Grissom and Reliant). So ships as big as Kelvin COULD have existed that time, and we just didn't see them. Starfleet was certainly capable of building such large ships.
I don't mind Axanar's smaller "kelvin-style" ships TOO much (the newest versions we see in the trailer are perhaps suitably differently-styled than the Kelvin) except that with their proportions, they now have like... 3.5-4 deck saucers, which would be dwarfed by even the NX-01's saucer.
With an almost identical saucer deck count, the Kelvin's saucer was pretty clearly designed wider
, but not thinner
than a TOS saucer, so when it's shrunk down like this, we get a wafer-thin saucer.
Maybe if they lost the "ridge" that runs around the upper side of the saucer. That'd be the final push that would tell us "these are not the same components as the Kelvin", but the shapes (such as the circular, non-teardrop bridge module) would still hearken to the Kelvin.