> one thread being that it mixed temporal and spiritual concerns instead of making them obviously distinct
That's really, really, not something Christianity gained from Rome. Judaism is, and always has been, a religion of the practical world. It prescripts how to live, from the very beginning. The Torah is very concerned with the answering of how to live, as well as the why to live that way.
Good point, yes, Christianity came with its own judaic heritage.
But without the centralised, territorial organization, administrative structures, cultural tools (especially Latin) and normative legal framework from Rome, the Church wouldn't have had the means to influence consistently so much the society of its time and the ability to support and control a spread that extensive through Europe and further.
By choosing Christianity, Constantin found a way for the Empire to survive into something different. And Christianity gained a tremendous powerhouse to use and adapt for its own growth.
And my point is that this hybrid huge "thing" is more driven today by its institutional heritage than spiritual's (otherwise, it would act vehemently more about its power abuses, sexual abuses, and terrible understanding of marital life, if only for pastoral care). And that's because it's much more a man-made (and male-made) organisation rather than one guided by God.
That's really, really, not something Christianity gained from Rome. Judaism is, and always has been, a religion of the practical world. It prescripts how to live, from the very beginning. The Torah is very concerned with the answering of how to live, as well as the why to live that way.