The idea that ideas survive through pure chance is as nonsense as saying mathematical equations survive through pure chance, or combinations of numbers survive through pure chance. An idea which is universal never dies nor mutates.
Rubbish - many ideas take hold because they appear at the right time and the right place - so by chance they are able to perpetuate and take hold. Others simply vanish because they never had that good luck.
And the same applies for leading people as well as ideas.
You might want to read Malcolm Gladwell's 'Outliers' - a great book which explains why hard work isn't enough on its own to ensure success (whether of a person or an idea) but that good luck is also essential. He uses some great examples to show this, for example:
The fact that most high level sports leagues include players biased toward birthdays in one half of the year - why because at the earliest stage teams are based on year groups with (for example) a 1st Sept to 31st August cutoff. For the very young there will be a massive difference between a Sept born and August born child in the same 'year' and those older kids seem better and get the opportunities - pure luck of birth date.
That virtually all the successful corporate lawyers in 1970s New York were jewish from the same area and virtually the same age. Why because by luck they were born into a small generation (low birth rate), by luck were a generation who benefited from high quality public schooling in the 1940s, by luck they were excluded from the established 'WASP' legal firms and had to set up alone, by luck they were just at the right time and right place for major changes in corporation law that they understood in the 1970s and the established 'WASP' legal firms had ignored because they thought this kind of work was beneath them. So they cleaned up - virtually all the most successful being almost identical demographically, and the reason for their success - good luck. Had they been born 10 years earlier or 10 years later they wouldn't have been successful. Good luck abounds.
So how does this equate to the success of christianity. Well I think it benefitted from two major elements of good fortune, both of which relate to the Roman empire. First the presence of the empire throughout the Mediterranean and southern europe allowed people and ideas to spread in a manner that would have been impassible had there not been a unifying empire across that region. And secondly they hit lucky as just at the time when tiny pockets of christianity were becoming established through that empire, the need to deal with a slow decline in the empire by the 4thC meant that they encountered an emperor ripe for new ideas to try to reinvigorate the empire and stop the rot, and was receptive to the idea of a new religion.
Without either of these, and noting that christianity failed to take root in the place and time of its inception, then I doubt anyone would be talking about christianity today - and as with the Gladwell examples, both of these elements of good fortune for christianity were just luck.