There are lots of reasons. As I know, with low power supply:
(1) the output swing will be limited.
(2): usually, the channel length is short for low powe supply, which will affect the gain.
(3): the SNR is another reason
Re: Why low voltage/low power is difficult to relize in anal
Hi
Most digital elements work in the CMOS tech. the information that is passed is normally a low quantitie of charge and that is it (the actual transfere by writing a "1" is approximately charging a very low F capacitor) - current is almost not invovled in it. Hence - the transistors works in either OFF or in the Saturation - non in the linear zone. The actual bits transfere will be either pulling down a fet-gate, or releasing it - actual current are very very small. Another good mesure to see power consumption in the digital components - the same IC, the higher bit rate - the more power (BIT-RATE = F*Q = more power).
In the analog IC: The main requirement is "LINEAR" - to be in the Active operation mode. that requires, in NPN - Vce>0.2v - most likely about 0.5 - 1v (difficult to get LOW voltages). The other thing - Analog ICs are all about "give me signal, and current". The requirements for S/N ratio (in analog terms) is much more strict than in the digital sense. I am sure you can speculate it more...
Re: Why low voltage/low power is difficult to relize in anal
Limitations due to LVLP:
the reduced number of the stacked devices, the reduced linear voltage swing, and the difficulty of turning on the MOS switch over the entire voltage swing.
I think the main reason is the lower supply voltage limits the output swing to be small while the noise level is still the same.
In other words, the Dyanmic Range is small.