Then tell that to India, China, and Japan. They have many gods, but also organization as well. It is possible for the Roman Empire to go the route of the Japanese Shinto system where the Mikado is also the chief miko / shamen - and a claim of descent from the divine much like Julius Caesar claimed descent from the Goddess Venus and Jupiter.
This is quite common misconception of depicting Japan and China as a surviving polytheist states. This is largely incorrect.
Both are in historical times primarily a Buddhist - which is
northeistic religion (i.e. religion which do not explicitly declare existence of any gods). Popularly perceived as "Buddhas gods" are rather closer to definition of Christian saints rather than any gods in polytheistic tradition.
Polytheist Shinto is actually should be grouped not with the ancient polytheist religions, but with the New Age religions like B`hai, LDS church or neo-paganism because Shinto was completely new religion invented in 19th century on the wave of nationalist and anti-Buddhist popular sentiments, just reusing some of allegedly Old Shinto practices been extinct for about thousand years.
Historically, polytheistic systems had difficulty competing with both monotheistic and northeistic religions, simply because too many would-be followers gave up tracing intricate connections between different gods. The
monotheistic and northeistic religions had quite small difference in learning difficulty for most believers, and therefore these 2 types religion types (as opposed to 3rd type of polytheistic religion) do inevitably dominate majority of world religion followers is soon as suitable communication means for proselytising (i.e. written books) are available.
The line between religion types is blurred though. For example, Christian tradition do include all three types - polytheistic (Arianism), monotheistic (Trinitarian) and northeistic (Deism), which come to prominence in in different periods.