From sculptures to coin images of emperors, it seems like from the 4th c. onward many of them had unnaturally large eyes. Why was this? Did the artists just suck at facial portrayals or is there a reason for, or meaning behind, this?
Political artistic representation of the Late Empire tends to have an "super-realistic feel compared to classical realism, in part because the political and cultural crises of the IIIrd century allowed experiment outside canons, with even some experiments on what could be considered part realism, part expressionism.
A new importance was given to symbolism, not just on actual, concrete symbols like victories and toga, but on descriptive symbolism.
It helped that regional particularities began to affirm themselves there and there (while the evolution, within a declining material context would really continue during Early Middle Ages).
It's not just a matter to convey specific messages (although the lack of real facial particularities on the sculpture of the Four tetrarch certainly conveys the idea of a collegial and essentially equal and unified imperium, for instance.) : decorum was taken to brand new heights and mosaics knew their golden age trough the period, with a similar insistence on super-realism.
I'd say the reasons are to be found in the crisis, which quickened for cultural and ideological reasons a change of tastes among elites.