Actually it doesn't. It really doesn't.
In American Navy building practice, it has been common to build ships larger and larger because larger ships are easier to modify and keep in service longer.
We don't know if the Excelsior is a relatively large design for its time our not. As of Star Trek III, we'd seen the Constitution class, the Miranda, the Excelsior, and the Olberth. That's it as far as Federation starships go.
In the near future it may be common for the US Navy to build
smaller ships.
I'd like to see some evidence for your off-hand claims about build-sizes, service, and modifiability.
As for the last point (modifiability), it has already been established (in-universe) that Starships are highly modifiable. Throughout the life of the original Enterprise, we saw it go through many modifications. Moreover, it seems to be very common that starships have a modular design (allowing one to swap out nacelles, for example), which is conducive to modification.
The pressures that determine the sizes of ships are often contingent. At different times, different sizes of ship will be more competitive. If US Navy ships used to tend to be smaller, there was probably a pretty good reason for it. If it was a simply a universal truism that the biggest ships are the best, we would see navies always building big ships. But they don't. Different navies have different needs. Different times have different technologies and strategies.
Also, seeing how modernization so often entails miniaturization, it hardly seems to be a truism that bigger ships have a competitive advantage.
Moreover, many larger ships have proven to be design failures (see upthread), precisely because they are so large.
In short, no we cannot simply default to the idea that "bigger is better" is some sort of universal truism that proves much about why the Excelsior succeeded.
Larger ships also offer more damage redundancy and resistance to damage without the use of heavy armor.
Starfleet ships have shields, energy shields. They do not defend themselves from attack in the same fashion the ocean going warships of yesteryear do.
We have learned, for example, that the Defiant is a "tough little ship."