That would be a dangerous strategy for Hannibal as Carthage also had slaves. Once the idea of slave revolts gets planted, it might be hard to stop it spreading.
Cheers,
Nigel.
Cartago can live without slaves much easier than Rome, depending more on the Sea than on it's Hinterland and agriculture, although that started to change after the first war.
Hannibal never managed to get Romans allies and tributees in Italy to join him, despite some of them had suffered hardly from the Romans.
(Remember, Roman Citizenship wasn't granted to them yet, I think it happened when Lucius Gaius Ceasar (Gaius father) was consul.)
And he probably wouldn't have Gladiators, who made up the core of Spartacus' uprising.
A siege of Rome doesn't promise much success.
Hannibal wasn't prepared for it.
But if we consider that he spend 17 years in Italy, maybe if he besieged Rome with 2/3 of his forces while the Rest ravenged through Italy securing food for those besieging Rome?