Dynamic compression in speakers themselves?


The primary audio characteristics I want to achieve in my system is an open, uncompressed, unstrained, and highly dynamic presentation.  What I don't know much about is how much speakers can or do contribute to loss of dynamics and impact.  I have a very powerful amp, but it seems that when I increase the volume, yes, the speakers get louder, but perhaps not commensurate with the increase in the volume control.  I do think I understand that this type of presentation is more easily achieved with larger scale speakers, but even with my large speakers, I feel something is wanting. 

I guess my question is, what factors contribute to any compression occurring in the speakers themselves?  Also, can the age of a speaker cause a loss of dynamics?  Mine are ~20 years old.  I'm thinking to get new speakers in the foreseeable future, so I'd like to understand more about this.  This question is in regard to traditional dynamic speakers.
mtrot
Agree with all the posters who stress high efficiency.

The day after hearing it, fourth row center, at Lincoln Center, I demo'd Tannoy Churchills with a Krell FPB600 and Stravinsky's Rights of Spring.

The dynamics were as good as the live event.  So ... it CAN be done.
If you want open sound , do as I did and try open baffle speakers . Spatial Audio M3 Turbo S in my case . High sensitivity, about 95 dB , Pro Audio drivers, 15" pair per side, compression horn from 300Hz on up & affordable factory-direct with a return policy you will not want to use . Better cooling of the voice coils not enclosed in a cabinet . Positioning is non-critical .
I have been experimenting with mechanical damping on both speakers and headphones using sorbothane glued to the front  speaker baffle or various locations on headphones. This can give an amazing increase in dynamics and improvement in timbre.  What is happening here is barely discussed among audiophiles but as best I can tell it is just Newton's third law in operation. For every action there is an opposite reaction which means that the vibrations coming out of the speakers create an opposite set of vibrations in the enclosure. Dampen these out and  you get a striking, almost amazing improvement in sound. About a half dozen headphone makers  are playing around with this, including Sennheiser, Grado and B&W. The last time I Googled "constrained damping" I came up with a similar number of speaker manufacturers. I discuss these issues in greater detail here.  https://www.head-fi.org/threads/damping-mechanical-energy-distortion-of-stax-and-other-phones-with-s...  This damping results in some loss of efficiency.
Other speakers: Legacy Focus is good value and great performance. Large Focal good also but expensive. Paradigm Persona 9H. B&W 800. Pretty much the top of the line in any of these brands will bring you quite close to pro main monitor - you will only miss a few dB dynamic range. Unfortunately, nothing really gets around the physics of a giant box with big woofers - you can’t have small aesthetics without taking a little hit in dynamics.
http://www.ajaudio.co.uk/Loudspeaker%20thermal%20compression.htm   Thermal compression is a term used to describe the effect on a loudspeaker of the voice coil heating up during use.