If a speaker is NOT time coherent, the fundamentals and overtones do not arrive at the exact same instant in time. The overtones arrive a little bit later. My understanding is that this does reduce the perceived dynamic contrast a little bit. (Note that a speaker can be "phase coherent" without being "time coherent". It’s not hard to put the drivers in-phase in the crossover region and claim "phase coherence", but among passive crossovers only a first-order crossover can be time coherent, and if the drivers are non-coincident, the system is only time coherent at locations where the geometrical relationship between drivers and listener falls within a narrow range.)
Of far greater impact on system dynamics, in my experience, are thermal and mechanical compression and thermal modulation (the latter being the short-time-constant, but much less-well-studied, companion of thermal compression). These effects tend to round off the peaks. Thermal effects are typically negligible when a driver is only seeing a very small fraction of its rated power handling. Mechanical effects can arise from suspension system or motor system limitations at high power levels, and from suspension system hysteresis at very low power levels.
The generally superior dynamic contrast of systems with prosound-capable drivers imo indicates that their negligible thermal compression, thermal modulation, and mechanical compression at home-audio listening levels are solving the most significant problems. Very expensive and/or multiple "hifi" drivers can sometimes achieve similar dynamic performance.
Duke
