Are you talking about a specific 'sack of Rome' as in 387 BC and 410/455 AD? Or generally the 'sacking' of a major city in the Roman Empire, such as Mogontiacum/Mainz or Colonia/Cologne?

In the Vandal sacking of Rome in 455, the aqueducts were destroyed, which would have cut off water the whole population. It is unknown how many Romans were sold into Africa by the Vandals, but the possibility was a cause for concern for the common man as well. While brutality of the 455 sacking relative to similar attacks is disputed, it definitely would have included some degree of the murder and rape that accompanied the ancient sacking of a city. Even under your assumption that the most significant loss of such a raid was the gold, the loss of the wealth of the upper class has profound economic consequences for the whole of society. The aristocratic class did not use their gold to admire their reflection or swim in it like Scrooge McDuck or Smaug. They used their wealth to buy things, build public works, and protect the city, all of which employed and benefited the lower classes.