Why is auto transformer is not used as a distribution transformer?

They can be. The benefit of an auto transformer is it can be made smaller than a traditional transformer and have the same power rating - this is because some of the power in an auto is transferred via conduction, while in a traditional transformer all power is transferred via induction.

If the voltage ratio between High / low voltage is much above ~3, this size savings is lost. The highest ratio I've seen in an auto is 3.33. Many distribution Transformers convert voltage from 30-70kV to 2.4-13.8kV, so for many cases you will end up with a ratio in the 4-10 range, although I have seen some as low as 2.5.

Another Answer

Autotransformers are not used in the secondarydistribution system -i.e. they are not used to step down a high-voltage distribution voltage to a low-voltage distribution voltage- for two reasons.

Firstly, they do not provide electrical isolation between the high- and low-voltage systems. This is essential, for reasons of safety.

Secondly, should a break occur in the low-voltage part of the winding, the whole of the primary voltage will be applied to the load.

For this reason, autotransformers are restricted to transmission and (in some cases) primary distribution systems -i.e. they are used as power transformers, rather than as distribution transformers.