drivers have a habit of starting to do funny things around fs at high levels, like response peaking. (If anyone has a good explanation for this phenomenon, I'm all ears.)
Can confirm this from listening to many examples, but cannot really give a valid explanation. Seemingly drivers which are incarcerated into an enclosure way too small pushing the resulting resonance frequency to kick band (around 100Hz is worst) tend to show strange and unpredictable dynamic behavior at different SPL.
So, yes you can boost the level between driver resonance and port tuning to get a perfect FR, but it might sound different at different levels. One explanation might be the stiffness of air enclosed which combined with compression also tends to drift the port tuning depending on the level. Whenever I see minimum active driver excursion frequency drifting at different SPL, it is a big red flag.
So a driver that natively has less bass output (that being the higher fs unit) is also going to have less excursion, but you could achieve the exact same effect with EQ.
Certainly true for a sealed enclosure. For a reflex design which is non-standard, i.e. high resonance of the active driver and lower port tuning than calculated, the equation is changing as the port also shows decreased excursion, but distributed over a much broader frequency range. If you apply boost on such a construction you have active driver and port playing in parallel over a broad band. Not ideal in my understanding.
Fs is the resonance frequency of the speaker, so theoretically there is only low energy needed to make the system oscillate.
That is true, but usually higher efficiency, i.e. less energy needed to oscillate, is expressed in a sharp peak in impedance exactly at Fs, while the output level stays relatively proportional to input voltage. At least if the total quality factor is not overly deviating from the desires area 0.5...0.75
So, to apply all this on the OP´s initial question:
bigger dustcaps coming with a bigger voicecoil are just indicative of a different driver design. Same is true to high-excursion woofers as a measure of giving stability to the moving system. I am reserved when it is coming with shallow woofers or high-fs/Qts designs.
Regarding AnalogStephs comment on micro- and high-excursion drivers: It is indeed astonishing what modern driver designs can achieve. But I noticed that most of really capable units to produce bass from a small enclosure and little diaphragm area are actually showing a pretty deep and long motor design (may it be with a double spider or extended VC former or alike.
I don't get is how both concave and convex dustcaps can both work.
They are kind of the opposite, when it comes to the dissipation/radiation of sound waves, and a major part of the diaphragm when large, so how come they both work?
For lower frequencies, hence longer wavelengths, the diaphragm geometry is not really relevant, so they both produce a very similar wavefront. The shape of the dustcap or second cone is in woofers and midwoofers rather a question of rigidity and geometry of the whole design.
It is very relevant for upper midrange and treble, though, particularly with designs having no equally rigid diaphragm (like the aforementioned ATC, or BMRs), or driven by a large voicecoil with any diaphragm that is not completely stiff (as they show a tendency towards ring-radiator behavior).