There were two groups of fractions issued from Rome shortly after Constantine's victory:
1) VIRT EXERCIT GALL, PACI PERPET (Constantine only)
2) FVNDAT PACIS, GLORIA PERPET, SAPIENTIA PRINCIPIS (Constantine + Licinius)
The first group, per the Gallic army reference, is celebrating Constantine's victory, and per bust style was issued first.
The second group (Licinius, Rome+Trier, etc) is clearly distinct from the first and must celebrate a different occasion, which it seems would generally have to be the new accord between Constantine and Licinius (cemented by Licinius marrying Constantia). Since the SAPIENTIA type copies an Arles solidus type (also issued for both Constantine & Licinius), it suggests a date after the death of Maximinus II (who does not appear at Arles) in 313. It's tempting to connect these types to the "edict of Milan", but given that Daia was still alive at the time of Licininius' visit to Milan, they may have been issued a bit later, even if that is what the SAPIENTIA type alludes to. Alternatively maybe these are just celebrating the alliance?
The bare headed busts would seem related to the reason/occasion for issue, and seems to fit well with a message of peaceful accord and familial connection - the propaganda message seems to be that this is a personal relationship. There is also an unlisted Trier fraction (featured on the cover of one of Zschucke's books) with bare headed busts that may be related to same occasion.
I agree these are hard to find in high grade (I haven't even bothered to acquire them myself), but some like the ones below are decent, so maybe there is nothing unusual there. The SAPIENTIA reverse (esp. owl!) is often poorly done, but that seems mainly due to the size (with this one smaller than the other two).