Remember the classical Roman empire only lasted a few centuries while the Eastern Empire lasted about a millennium longer. Up until the 12th-13th centuries, the Byzantines were one of the few producers of high-purity gold coinage (or coinage at all) left in Europe. There are many more centuries worth of histamenoi nomismata and, after a revaluation in the 11th century, hyperpyroi. After the Fourth Crusade and declining Byzantine fortunes, the money ran out and they ceased producing high quality coinage.

I'm not sure what you mean by the "reign of the Constantines." Do you mean of Constantine I? He's enduringly popular due to being the first Christian emperor, and I suppose numismatic sites are driven by that sort of supply and demand, not what actually survived. The examples you see certainly weren't circulating for a thousand years after his death in the Byzantine Empire. And he wouldn't have been featured on the coins of his successors. They typically had a portrait of Christ on one side and then a portrait of the reigning emperor(s) on the obverse.

It is probably at least partially a factor of where they are being excavated. In my experience (which is 8 years of excavating in Israel) a very large number of Byzantine era coins are excavated from the southern Levant. More so than in other eras. We're talking hundreds per season at excavations which include remains of the Byzantine period. Later periods like this are easier to access, because they are closer to the surface, and therefore are excavated more often. Because there are so many coins, they are also easier to sell on the antiquities market. It turns into a case of there being a large supply of coins from the Byzantine period in the eastern empire. There are much fewer coins from other eras.

How are artifacts such as coins put on the market? Many countries have laws regarding how antiquities are dealt with. In Israel, for example, the materials belong to the government of Israel, and are only sold through authorized antiquities.

Israel has a number of authorized antiquities dealers who are authorized to resell antiquities such as coins and pottery vessels from the government, if they are considered surplus and unneccessary for scholarly research.

This is the Israeli law in question that deals with how they must bet treated.

This article outlines some of Italy's efforts in that regard as well, and Italy appears to have similar laws and perhaps more stringent enforcement.

It is possible that Italian antiquities laws mean that less coins from the western area of the world go onto the market. It is also possible that there are fewer excavations recovering coins in that area of the world (there are hundreds every year in Israel alone).

Finally, as u/michaelthedrunkard explained, the classical Roman empire was a bit shorter than the Eastern empire/Byzantine empire, and therefore there is more time for coinage to happen.

This is all from personal experience in the field of archaeology and dealing with these coins as they come out of the ground.