An LM317 uses 1.25V as reference, which in a current regulator circuit puts that voltage plus the pass transistor's own voltage drop as the total drop, which is quite large. I looked up low dropout regulators (Wikipedia), and saw that the same 1.25V bandgap reference was generally used. If that could also be lowered, perhaps to a tenth or even to as low as 50 mV via a resistor divider onboard, as well as using a FET as pass transistor, total drop in current regulators could be lowered further than usual. 50 mV seems small, but I think many newer PSU and LED driver circuits with small sense resistances imply that accuracy can still be had with low sense voltages.
Is a very low reference voltage used in 3-pin variable voltage regulators? If so, any specific devices I should look at, and if not, why not?