I’m not sure I buy Faulkner’s analysis, especially this part:

The men and women set on fire, eaten alive by animals, or nailed onto wooden crosses to die provided the Early Church with a roll call of martyrs as impressive as any in history.

I am not super familiar with the literature here, but it seems like a lot of this is resting on early church propaganda; see this thesis, for example.

When one goes beyond later Christian authors and examines the sources, both Christian and non-Christian from the early period, they do not point decisively to the conclusion that the earlier emperors were simply predecessors of the later emperors in their Christian persecutions. Although these earlier emperors received much attention in later Christian historiography, and they are identified as staunch persecutors of the Christians, these accounts appear to be biased and coloured by the events of the third and fourth centuries CE.

Re: Kautsky, I’m not really seeing how that relates to the earlier point that the emperor was bowing to the popular will. Is the implication here that the army became Christianized, and so Constantine had to follow suit in order to keep up appearances? I’m not seeing anything to that effect on the linked page. If the implication is that greater members of the aristocracy were joining up and that threatened the political feasibility of polytheism, then there’s a contradiction between that and the earlier point that it was the appeal of Christianity among the oppressed (per Faulkner) that lent momentum to the early Church.

Personally, I think Damascusart has the right take. It seems like conversion was more of a convenient way to consolidate power - something similar to Akhenaten’s establishment of monotheism in Egypt several centuries prior. Polytheism ended up winning and Akhenaten was practically erased from history after his death, so the question of why Constantine didn’t get similar treatment should be addressed, but I’m not seeing popular opinion as a credible explanation.