Long story short:
Conquest.
In the case of the original Roman empire, it might just have been historical coincidence that eventually put an exclusivist, proselytising faith in total control (leading to all other religions being abolished by penalty of death, their texts destroyed, their temples and holy artifacts destroyed or seized). Things could have worked out differently, but they didn't, and the Talibanesque antics of Theodosius "the Great" and the Churches existing at that time made sure that no competing world view could ever hope to resurface again. (This was also the time when neo-Platonist philosopher Hypatia was killed in Alexandria, putting a final end to antiquity and its scholarship.)
This is utter nonsense. Paganism died largely of its own accord and though not good for your career, Pagans weren't destroyed. To take an example here, we se Volusianus as proconsul of Africa, a practicing Pagan, in a high office at the start of the fifth century. Or Symmachus that petitioned Gratian to restore the Altar of Victory.
Temples were closed once there were too few pagans around, or too politically unimportant, as they were expensive public buildings best used for other purposes therefore. Sometimes this was not the case, but this was the exception rather than the rule. We see active Pagan temples in Rome during the sack of 410, and even later when Belisarius retook it.
Their writings certainly weren't destroyed. In fact the Iliad or Aenead, amongst many other Pagan works, remained the backbone of Christendom's Education syllabus until fairly recently
While Hypatia is given a lot of press, this is an isolated instance. The Academy at Athens continued to teach Neoplatonism up till Justinian closed it in the 6th century - more than 200 years after her. We still see Boethius continue the philosophic tradition in the West in the Ostrogothic Kingdom, too.
The Church is also responsible for saving a lot of it, from barbarians and the common folk that no longer saw much merit in it (not dissimilar to the cult of what is deemed 'practical' today, with philosophy and so forth denigrated for STEM fields).
The fact that it survived in the Eastern Empire and could be directly or via arab commentators, be reintroduced to the West, speaks volumes.
As for the rest of history, simply compare the distribution of Christianity across the globe to historical maps of Colonialist conquest and the accompanying (cultural and actual) genocides. Religion was instrumental in this era of atrocity right from the start, when Spanish conquistadors exterminated whole civilizations in the name of the cross. This method was refined over the ages. The usual M.O. went like this:
Send missionaries who build schools as a "gift" to foreign nations, starting the process of assimilation. Then, wait for one of two things to happen:
1. You indoctrinate a sufficient number of locals to support your claims to their country ("The Pope has decreed that you are now subjects of the Spanish crown.")
2. The locals try to fight back, prompting you to retaliate with all military might against this vicious attack on "innocent Christians just wanting to do the right thing".
To my knowledge, virtually the only place to escape this trap was Japan, where the Shogun was warned by the Dutch against the subversion happening right under his nose. The result was gruesome indeed, with all Christian converts being executed and the shores of Japan being closed off to foreigners for several centuries, but it definitely saved that country from sharing the fate of the Philippines or others.
This is a fairly specious narrative. Forced conversion certainly took place, but the situation is very different from what you describe.
We see Norse or Slavic conversion occuring without conquest, and the conversion of much of Africa without compulsion.
India was not forcibly converted, nor Africa, nor Indonesia. They had long periods of Christian rule. The Europeans massacred African populations, but sent in missionaries mostly. Look at the Dutch in Indonesia and South Africa, for instance.
The Spanish are a special case, but even here people like Las Casas pleaded for clemency, and the Church often acted as the protector of the natives. This is why clerics are so well represented in independance movements from Spain.
As to Conquistadors destroying the cultures of the Aztec or Maya - so what? That was thr moral thing to do, as these were cruel, murderous cultures drenched in human sacrifice. Like English suppression of Sati or the Thuggee cult, this is not only morally excusable, but called for.
But yeah, in all seriousness, we tend to overlook the way in which innovation was considered undesirable in antiquity. Here, have another treatise on Plotinus... and another, and another. Whoever has the most faithful commentary on our favorite centuries old luminary wins, but whatever you do, don't be original.
