The reason why rationality can’t compete with belief is that rationality assumes WHAT reality IS and then deduces HOW reality WORKS, contrary to belief which instead confuses assumption with deduction (ie, isn’t rational).
The only possibility for rationality to compete with belief is to assume HOW reality WORKS and then deduce WHAT it is, but it is impossible to assume HOW something WORKS without assuming something about this “something”. And, even if had been possible, the deduction would have been ambiguous, as Russell’s paradox tells us (as in finding the primitive function in mathematics), ie, that that “something” then could have been more than one thing.
Rationality is thus doomed to walk around belief like “a cat around a bowl of hot porridge”, as we say in Sweden, just because it is rational (ie, does not confuse assumption with deduction). It can serve many needs, but not that of an ultimate explanation of what the world is, or what and where we came from. Such questions must instead be submitted to belief (and all possible answers are contradictory).
This fact may be sad for some rationalists, but the light in the tunnel is that the fact isn’t an insurmountable problem for mathematics, but has instead already actually been surmounted by ZFC (in finite mathematics), meaning that we actually can calculate on a reality that we can’t understand. This allows us to find solutions we don’t understand (other than mathematically) on problems that appear rationally insoluble. We can thus climb further on the ladder of what we can do, without actually understanding why it works (other than mathematically). This is what the fundamentally engineering rationality can achieve. It can’t explain what reality is, but it can open surprising doors in the matter of what we can do.