What about speakers that are good at rock, but also sound very good at mid to lower volumes?
There are a great many speakers to choose from at low to mid volume capability levels - most of them sound excellent. A good audiophile rock speaker will also sound excellent at extreme SPL's (the added capability). Whilst ordinary or low cost rock speakers may not sound very good at all (just play loud).
It is simply much more expensive to build an "audiophile" quality speaker that plays very loud. You may have to compromise on exotic wood cabinetry (expensive) and get an ordinary black box with pro audio drivers (expensive) that is all. An extra thousand dollars in manufacturing cost that would have gone to veneer goes towards expensive drivers instead of cheap ones ($600 woofer instead of $100 and $600 mid instead of $100).
Is it something about their design
Yes it requires a compression horn driver OR a super robust conventional driver (short coil long gap and huge magnets). There are specific design choices needed to play cleanly at loud dynamic levels, such as dealing with the high levels of heat generated in the voice coil (causes compression). If anything the speaker will be voiced lean in the bass, as bass sounds stronger at elevated levels but is nearly inaudible at low levels (Fletcher Munsun curves).