Speaker driver sizes - pros and cons

I don’t think you’ll find a 12” driver that is actually considered full range. Those larger drivers are normally used for PA applications and their frequency response is within the midrange band. Anything larger than an 8” driver will require a crossover to a tweeter. That’s been my experience when trying to build my own single driver (audiophile) speakers. YMMV. 

timlub, with all due respect I do not agree for several reasons:
1- Mass is always an issue.  Larger motors do help, but the reaction time also increases; larger motor or not.
2- Mass vs motor: over-driving the cone is typically only a concern with larger speakers.
3- Larger speakers have more issues with wave propagation timing and scattering effect.

I have owned and heard lots of great 12"-15" speakers.  But in the same family, for example, I have never heard a 15" cone driver resolve more midrange and top end information than an 8' version of the same driver.  All things being equal and in the same family.  More bass, yes.  Better response across the entire bandwidth, sometimes yes but no more often than not.

My assertions above assume we are limiting our discussion to dynamic drivers and not compression drivers, correct?

@br3098 
In general, you are correct that a smaller driver is normally faster than a larger, but as I stated, A Properly designed driver: 
Mass is not always an issue,  understand that adding mass increases qms/qts,  adding mass decreases sensitivity... If you add a softer material, you'll find a more rolled off frequency,  if you add a hard material, you'll find extended frequency response,  The material added matters as well as if you coat the entire cone or add to the dust cap or even the rear of the cone.  
I'm really not stating an opinion. I've proven many times that a properly designed larger driver can be as fast as a smaller driver. 
I'm not sure what you mean by "over-driving a cone"  but proper cone, voice coil, excursion limits and even dust cap can produce a larger driver that extends well into the midrange, no doubt, depending on the final speaker design, you can certainly have beaming or lobing effects. but I have built and know where a set of speakers are right now that are a 15 inch 2 way that do a great job,  all drivers are custom modified for a natural rolloff at 1800 hz and when set up correctly,  they are excellent. 
Your overall premise that a smaller cone extends frequency smoother than a larger cone is correct.