An answer to a related question mentions that it's possible for dual US citizens to acquire an ESTA without lying, however it's likely that the authorization would be revoked shortly before their flight.
This begs the question of what is the maximum penalty for a US citizen who lies on the ESTA form (by omitting the fact that they are dual US citizens) and then proceeds to enter the country under VWP using their second passport? Obviously they cannot be deported or banned from future visits, but what about monetary/criminal penalties?
A related question shows that no real penalty exists for entering/leaving the USA with a foreign passport, so perhaps it's also legal to misrepresent yourself on the ESTA form.