Low efficiency and heat generation are the two biggest shortcomings of using linear regulators versus switching regulators for applications with high input/output voltage difference. These two things is used to prevent the usage of linear devices in many applications, specially in those with low power consumption requirements. However, the option of using linear LED drivers to address backlighting applications does not imply low efficiency for the case of PDAs and cell phones.
The figure above shows us about how a linear low voltage drop-out (200mV) LED driver such as the NUD4301 device can be implemented to address backlighting applications. For more information about this circuit, you can find on this paper. [Source ON Semiconductor]