Why do you think that? It seems fairly clear the mass appeal of the mystery faiths was growing almost exponentially in the Mediterranean world by the mid 1st Century C.E. Christianity had the advantage among those rising faiths in having apparently most of the best minds of the times, and developing the best "tool" kit for proselytizing. Nothing is certain - at least if you don't believe in determinism - but some directions chose are much more highly likely than others.
I've been listening, lately, to
this lecture on the rise of Christianity with a Professor Kenneth Harl and one thing he makes a big deal of is that's it's NOT fairly clear that the mass appeal of mystery faiths was growing. He spends an entire lecture making clear that, in his expert opinion, what we are calling mystery cults were nothing new and existed, not just in parallel with traditional polytheistic faiths, but embedded within those traditions. The Eleusinian Mysteries, for example, are literally Archaic, older than the Classical practice of traditional Greek polytheism itself. Others, like Serapis and Isis, are much more evidence of Hellenistic syncretism than of declining traditional paganism.
Christianity wouldn't have
gone away without Constantine's conversion, in Harl's view, but it wouldn't have necessarily risen to dominate the Greco-Roman and post-Roman European world. Traditional polytheism was vibrant and healthy well into the 2nd century and the slip in its vitality in the 3rd century and into the 4th had more to do with the general slip in Roman institutions and culture during the crisis than anything specific to the religion. There's no deep reason to suspect a recovery in the former wouldn't be accompanies by a recovery in the latter.
I am not expert enough on the subject to tell, definitively, whether Harl's views are just eccentricities, outside the mainstream of scholarship, but they present a pretty serious challenge to the picture of late Roman polytheism as anemic, desperate to be replaced by something more vital.