I do not know of a tight, simple relationship between speaker impedance and efficiency (or sensitivity)--in part because the terms are used as averages over a speaker’s entire performance range and a lot gets lost in the wash--but despite this, thinking in terms of the latter (efficiency) can help in understanding the role of the former (impedance). In practice, speakers with low impedances are current-demanding, and this is manifest in low efficiency, meaning that at the frequencies where the impedance is low, it takes more watts to produce that same dB level than where the impedance is higher. Now with this in mind, consider the adage that you can have any two of the following, but the laws of physics--at least how we currently know how to engineer within them--prohibit us from having all three. The three desirables are:
1) High efficiency
2) Small driver size
3) Deep bass
Since we can get any two in any number of speaker designs, let's ignore speakers that would give us only one or none (these speakers exist: see you local consumer electronics store). There are only three ways to get any two of the three above properties, and I delineate them below. (In the points below, I use terms like "high" and "low" and "deep" and "weak" relatively--they are just meant as short-hand to describe to the basic trade-offs and should not be interpreted too absolutely.)
a) High efficiency, small driver, weak bass speakers. Small drivers with weak bass can be built with relatively small magnets, and thus they do not need to pull serious amperage. If you listen to acoustic bluegrass on a 3 watt 2A3 SET with a single driver speaker you can get superb musical reproduction. The purist approach of the single ended triode will complement the inherent time-coherence of the single driver, and you won't miss a beat of sub-70Hz bass because your source music doesn't have any! Perhaps only a little exaggeration in jest in here, but basically, there is a real niche for "weak bass" speakers given the advantages of being able to drive them with just a few Class A full-glory tube watts at high impedances. So this is clearly a high impedance application.
b) High efficiency, large drivers, deep bass. Large drivers (e.g., large in diameter) can be driven by relatively low current magnets because the driver can create a leveraging action, either physically with a large diaphragm or acoustically as in horns. So if you have the space in your room, you can get high efficiency, high impedance speakers with deep bass. Avantgarde Solos go to 30 Hz at 97 W/m/dB in a nominal 8/16 Ohm package.
c) Low efficiency, small driver, deep bass. For a small driver--(and again, "small" here is relative; I don't mean literally small as in 1" or 2", I mean "not large," as in not Avantgardes)-- for a small driver to create deep bass it needs to move a lot of air via a deep throw, and this requires a powerful and relatively heavy magnet. Powering this magnet will require current proportional to its work, and thus the "low efficiency" rating. Clearly, high impedance here (i.e., high AC resistance) is not good, since that only exacerbates the current demands, so low impedance is better: open that pipe and let the current flow! Now the market for not-large, deep bass speakers is, of course, huge. In fact, I'd guess that more audiophiles at some point in their career have gone this route than any other. Many, many speakers are moderate size and seek to deliver deep bass. I'd be interested to know how many full-range, moderate sized, true 8 Ohm speakers are out there that can really reach deep bass without a sub.
So why 4 Ohm speakers? Because if you want produce deep bass in a small enclosure you are going to have to put some demanding magnets at the end of that amp; these magnets are going to suck juice. So far, we just can't figure out how to do it any other way.
