A starship has to move, both under warp and some form of sublight drive. Additionally, we have to consider that there may be limits to the volume that the warp engines can enclose. Just building bigger engines may not work if you can't build reliable field coils to generate the warp field, or can't built a power plant that can reliably provide enough energy for that engine etc... etc...
The fact that these ships exist in the Kelvinverse tells us that, from an engineering standpoint, none of those are valid objections. SOME version of Starfleet has the technology to build starships on that scale, which means the technology existed in the 23rd century and was within Starfleet's capability. Meanwhile, the Prime Universe is now introducing the USS Shenzhou, which is already (we believe) considerably larger than the TOS Enterprise and pretty much makes this entire thread irrelevant.
Lastly, there's NX-01, which a hundred years before the Constitution class was only about 30% smaller. The size difference shrinks even more in NX-01's semi-canon refit configuration with the secondary hull slung underneath; it tells us that the Federation was capable of building ships about as big as the Constitution even a century earlier, at a time when their nearest rivals already had much larger vessels in service.
Engineering isn't as simple as many non-engineers think it is.
Sometimes it is, though. The fact that both the Kelvin and the NuEnterprise have warp engines that are proportionately MUCH larger than they are on smaller vessels of the same era tells us that, yes, you CAN solve that problem just by building bigger engines.
More importantly, we can plainly see that 24th century designs reach similar sizes as the Kelvinverse designs, but manage to do so with comparatively tiny engine installations. The Enterprise-D, for example, not only has a greater overall volume than the NuEnterprise, but a far greater portion of that volume is useful space for the crew; something like 30% of that space is engineering and machinery, compared to about 60% on the NuEnterprise. And even a comparison between the Nova and Constitution classes yields similar parallels: Voyager has a greater volume than the TOS Enterprise, but still has much smaller warp engines, a larger shuttle complement, greater firepower, better sensors, a much higher top speed, and can operate for years at a time with a crew of only 150 (compared to 400 of the Constitution). These are all technological improvements that have nothing to do with Starfleet's ability to build ships bigger.
In THAT sense, you're correct that engineering isn't that simple: it isn't a question of size, but efficiency and composition and the capability of the technology you can install on a vessel of a particular size. Just because an older ship might be the same size as a brand new one doesn't mean they have the same capabilities.