That question also has occurred to me, and it is worth asking. As so often, it is hard to get documentation for a negative. The possible answer I thought of was that, though the cult was prevalent in the legions, and there are Mithraea as far
west, at least, as
London, and numerous paintings and sculptures relative to the cult (while not works of
genius) are obviously professional, its very absence (and a couple of instances would not alter the general statement) testifies to its hardly penetrating the socio-economic classes who determined the iconography of coinage (especially if it is equally absent from Gallic emperors' coins). In other words, the legati didn't embrace it, at least not openly,
still less the senatorial class in
Rome or, perhaps, the formally educated generally. In this respect, it contrasts to the prevalence of
Isis and Serapis. The Odessan Great God, like
Isis and Serapis, was at
home in the Hellenized world, and so were numerous others, such as Mên, but it looks as if Mithraism
had not deeply penetrated worship in urban (urbane) Greco-Roman life. Granted, but for the rise of Christianity, which did gain a toehold (and probably earlier than
Helena), Mithraism and other dualistic beliefs concerned with personal salvation might have prevailed in the 4th century, since it
had spread so widely. That is, of course, a matter of opinion.
As to
Sol Invictus: I think that, if they
had intended Mithras, they would have given him a Phrygian hat or some other obvious attribute; of course, Mithraism and worship of
Sol Invictus were not mutually exclusive, and both gained currency in the same climate.
Pat Lawrence