The Roman empire was thoroughly monetized.
The relevant event took place in 79 AD, long after the end of the Bronze Age in the Mediterranean.
You can definitely have organized society without banking, but AFAIK there was no organized society without some form of taxation, and few organized societies without long-distance trade (only in isolated places).
From the Code of Hammurabi (~1750BCE):
> If a man rents a boat of 60-[kur] capacity, he shall give one-sixth [of a shekel] of silver per day as its hire.
At this point, a shekel is a unit of weight, not a coin, but is already being used as, effectively, money. Coins were initially more a convenience thing than anything else.
Primitive banking-type activity is also showing up in this time period; institutions, mostly temples, taking deposits and lending with interest. And really, for most of the world (Ancient India did have some _slightly_ more sophisticated bank-like behaviour), that’s more or less where it stayed til the 17th century or so.
Bronze age civilizations had money. Coins as we think of them became widespread in the iron age. Shekels, for instance, go back much further.
There is ample written evidence that Bronze Age civilizations had money and here's just one example.
Ea-nāṣir!!!!!
https://www.archaeform.de/wordpress/blog/2016/03/30/worlds-o...
There is simply nothing among the finds that could be money, and contracts seem to be in the form of I gave you 18 measures of wheat for three fat sheep. You gave me 7 jugs of oil, and I will make you 8 pairs of sandals" (all numbers and everything made up right now)
He asserts multiple times the existence of banks, money lenders, and multiple written records of persons demanding payment of money in his book Letters from Mesopotamia, Official, Business, and Private Letters on Clay Tablets from Two Millennia: https://isac.uchicago.edu/sites/default/files/uploads/shared...
Do you have an alternate translation?