Suppose the church gave us the Bible?

A common Catholic objection against evangelicalism goes like this: Why do you trust the Church to give you the Bible when you don't trust the Church go interpret the Bible?

Of course, that's a loaded question:

i) The church didn't give us the OT–Jews gave us the OT.

ii) We don't accept the Tridentine canon of the OT.

iii) The ancient church disagreed on the scope of the OT canon.

iv) Which church gave us the Bible? The Catholic church? The Orthodox church? These can't both be the One True Church®

v) It would be more accurate to say Jewish and Christian scribes gave us the Bible.

That said, I'd like to consider the claim for the sake of argument. Suppose "the Church" did give us the Bible. Would it be arbitrary for evangelicals to trust "the Church" in that regard but not in regard to the interpretation of Scripture? Put another way, assuming (ex hypothesi) that God infallibly guided the ancient church to canonize the right books, is it arbitrary to deny that God infallibly guides the church in other respects?

It's customary to distinguish between miracle and providence. The fact that God performs miracles is not an all-or-nothing proposition. It's not a binary choice between believing that God always performs miracles or never performs miracles. In general, God performs miracles less often than not. Events typically occur according to ordinary providence rather than miraculously.

So even assuming, for discussion purposes, that God supernaturally guided the ancient church to give Christians the right Bible, this carries no presumption that God supernaturally guides the church in other respects, or that God continuously guides the church. In principle, it wouldn't be arbitrary for evangelicals to grant that God supernaturally guided the ancient church to give us the Bible, but doesn't supernaturally guide the church in general. For we routinely distinguish between miracle and providence. The fact that God sometimes performs miracles carries no presumption that God constantly performs miracles. The fact that God inspires some writers and speakers doesn't presume or imply that he inspires every writer and speaker. Most folks are uninspired. 

Suppose for the sake of argument that it was necessary for God to supernaturally guide the ancient church concerning the canon. That doesn't entail that it's necessary for God to supernaturally guide the church in other respects, or to supernaturally guide the church on a regular basis. The ordinary course of nature is the default modus operandi. Miracles are rather exceptional. 

Even on its own terms, Catholic theology is very selective about when the church speaks infallibly. It doesn't treat inspiration as an all-or-nothing proposition. It allows popes, bishops, and priests to be in error in much of what they say.