I haven't really found any literature on this specifically, but I suspect it might have something to do with these statues being more of a uniquely Constantinopolitan development, thanks to the city's extraordinarily preserved classical heritage. You don't really hear about any similar vast statue collections in any other Eastern Roman cities during the Middle Byzantine period, so I suspect most of these statues were not mass produced, and likely were exclusive decorations for the capital.

This explains why finds are so rare, since Istanbul is quite lacking when it comes to the archaeological front, it is quite a limited surface area for any statues to be found, assuming they survived the sacks in 1204 and 1453.

You should also be careful ascribing dates to these statues from the names the primary sources give them. Statues were often given local names/attributions that were entirely incorrect. The equestrian statue on the Column of Justinian is a classic example. It was put atop the column by Justinian, but most Byzantine tour guides thought the statue was actually of Heraclius. Depictions of the statue before it was destroyed seem to suggest however that it was originally Theodosian. So the identity of these statues would often get confused or twisted for ideological purposes.

Many of these statues might not even have been fully original, since the early 5th Century it had become common practice to simply decapitate an old statue/bust and add a new head. Justinian's aforementioned statue might have been one of these, as it had a Theodosian inscription on it.

The only proper statue that may date from this period is the Carmagnola in Venice, which is traditionally believed to be Justinian, but it could be from a later date too.