Just how scarce are Byzantine coins in general, and Byzantine solidi in particular? Has anyone ever made a professional conjecture for how many are out there?

I suppose the most common solidi are those of Justinian or Maurice. But add up all the known Justinian solidi and what do the totals look like? In the hundreds? The thousands? The ten thousands?

Is this addressed in any published work?

no clue

The problem with Byzantine coins is that they were not as well struck as earlier Roman coins were. So there are not as many that have servived the ages.

Some Byzantine coins are so common that you can get them for $1 each, some of the bronzes anyway. I have seen hoards of even the gold coins from ca. 1200 where the coins were going for $300 each, so you know a gold coin that old at that price is very common.

The Byzantine Empire was at the crossroads of trade routes betwixt Europe and Asia, and figured significantly in trade until the Empire was crumbling for the last 100 years or so. So the early coins are very common, but some of the last issues ca. the 1450's are very rare.

Some of the early solidi are very common. I've had some discussions about them but I don't recall whether any studies were done to try and estimate the numbers. Ill have to try and remember.