Я абсолютно уверен, что и Бауман не считает это наказанием.
Baumab, Crime and Punishment, 27
In some of his laws Sulla, and after him Caesar, replaced actual and immediate execution by aquae et ignis interdictio, the
interdiction from water and fire which denied the wrongdoer shelter and
sustenance and made him an outlaw liable to be killed by anyone with
impunity. In other words, Sulla gave formal expression to the procedure
used against Postumius Pyrgensis in the iudicia populi period. In effect
he placed voluntary exile on the statute-book.
(...)
The, new penalty has been aptly described as a conditional death
sentence; if the condemned man remained in Rome or Roman Italy he
would be at risk. It can also be described as compulsory exile, looked at
from the point of view of a community which wanted to expel a
wrongdoer from its ranks; departure was how the community hoped he
would respond to the sentence of interdiction.
Вот с этим Келли и спорит; он считает, что ни в каком законе Суллы такое наказание прописано не было.