It... sorta' does? Church has authority by the numbers, so to speak. Weight of consensus and all that rot. Take the bible out of the church and it can make a new bible -- establish new canon, make new rituals, and so on it. Did it the first time (well, and many times after, really, depending on how you view denominational splits), it can do it again. Take the church out of the bible and... it's just a book. If that. There's been plenty of things over the course of years written in similar formats and similar messages to the biblical texts (many even claiming to be divine just as hard) without being given any meaningful weight... and given that the notable physical difference is one has a hefty organizational backing and the rest kinda' haven't...
I mean, yeah, "I've got more critters than you" isn't exactly the sexiest of sources of authority the world's ever seen (in fact, it's flimsy as the buggery), but it does a fairly hefty job once you start handing out the dakka.
Which... I mean, "size of (metaphorical) beatstick" is probably a decent measure, considering the subject? That's basically the bible itself's position, innit? Beatstick of infinite size == infinite authority, is the basic proposition. Difference being the bible just claims it, insofar as anyone can actually tell, and the church actually has proven willing to start breaking kneecaps (either literally or via social approbation or whatev'). Advantage: Church?