Because EVERY religion puts faith as the only proof required. The more unlikely the faith, the better it is, the more good you are.
Not true. This is mostly valid of semitic religions, which happened to spread over a huge chunk of the world, but several Eastern religions are belief-less.
For example, while there are some Buddhist sects that are belief-based, the older ones are all about experimenting, to the point Gautama told followers that if the techniques he was telling them didn't work, they should seek something that worked instead of losing time with it. In Japan, Shinto is so anti-doctrinal, anti-dogmatic, anti-theological and anti-moralistic, that it doesn't mind you not believing in anything at all and instead being a full-blown atheist who only takes part in its doctrine-less activities for cultural reasons.
As for other polytheisms, animisms etc., they also don't place that much importance in belief. Yes, they have it, but it isn't central. So much so, that when it comes to putting "belief" front and center, Christianity and Islam are really the exceptions to the rule.
Alas, the problem is that these minority of belief-based religions are the ones that are winning, so your argument has merit if we change the focus to saying that a religion becoming belief-based is a winning strategy on the long run. Why that's the case though, I have no idea. On the face of it, it doesn't seem to make sense, but maybe not making sense is actually the point...