Fashions change. Note that left facing busts become more common in the later 3rd century AD but often were fancy in some way that is not seen in right facing busts. Take, for example
coins of Probus with a great variety of
military and consular busts facing left but the majority right facing busts are all ordinary in comparison. By the Constantinian period we see left facing and fancy busts but many are used with younger rulers honoring their first appearance on the coin scene. It is easier to find a fancy leftie for
Licinius II than for
his father. It is almost as if the left
bust has become a sign of less respect than the simple right
bust just as a century before when a
head was used for the
Augustus but busts were used for lesser figures. Perhaps I'm no better equipped to understand this than to understand why it was considered a sign of greater respect to have ones name split in two on the
obverse legend as compared to being in a continuous
arc as used for lesser persons (mostly kids).
The reform that brought us the
FEL TEMP REPARATIO coins introduced the concept of the left
bust indicating the middle of three
denominations and is the only case where I really see a plan behind the left/right question. The
denomination soon died and after that we rarely see left busts at all. About that time we do get more facing busts especially on gold but that may not be related.
Other than the FTR coins, I'd like to know why some coins were made left facing in any given issue. In many cases there may be no reason. It seems certain to me that the reason for one issue may be in no way related to the reason for any other. In the cases of coins that were 99+% right facing (like Severans) I wonder what the
Roman on the street thought when he saw a leftie. Would it have attracted any notice or would it just have been something to spend?