Religion is like fiction (well, it is fiction), every plot hole gets a convenient explanation. For example, why didn't the
wizarding world in Harry Potter use their time-turners? They apparently only issue these magical devices to children who need to be in two classes at once; nevermind wizard time cops who could have stopped Voldemort from ruining lives. One explanation is that all of the time-turners were broken when a bunch of wizards got rowdy in the Department of Mysteries, where the entire world's supply of time-turners were kept. This happened before all of the big battles started, battles where time travel would have been helpful. How convenient. Any excuse you make is going to be flimsy, though, because the powerful time-turner was only intended to be used as a plot-device once by Rowling, and you can only respond to people explaining inconsistencies away with a sarcastic "how convenient".
Religion uses similar fluff to repair its "plot holes". Mormonism in particular is really damn full of them. Consider the Golden Plates. Why aren't they still around, in a sacred vault at Temple Square? Somewhere where their authenticity can be confirmed? It's really odd, isn't it, that religions that are just so certain of their own truthes leave artifacts and other evidence out of reach of secular validation (and perhaps instead rely on uncritically faithful and relatively uneducated "witnesses" with dubious accounts). No, the Golden Plates had to be taken up to Heaven by the angel Moroni, because how could they be left in the hands of humanity, even though humanity is the reason why they exist anyway? Couldn't God have just kept the "sealed" parts on planet Kolob and let humanity have this important artifact? How convenient.
You can say that leaving the authentic "Reformed Egyptian" tablets in the hands of the Earthly Mormons, thus proving the history behind LDS beliefs, would deprive people of their faith, since it would have been proven to them. First of all, it would only prove the historicity of Mormonism, and would be as much proof of the accuracy of Mormon beliefs as the Dead Sea Scrolls are proof of the accuracy of Christianity in general, so it wouldn't deprive people of their faith in God. Second, that might be an argument for Christian denominations that believe in Hell for nonbelievers (because if there's one thing God hates, it's people who don't believe things for no reason other than their own personal feelings), but in Mormonism, if you don't convert to the True Faith on Earth, you just have it proven to you after you die and are free to convert at the last minute. Thus, isn't it retarded to keep evidence away from religious seekers on Earth when they'll just get the proof they need in the Spirit Prison?
I've never gotten why God would insist on making it as difficult as possible for people to find the One True Faith. People always end up going with either their childhood faith or whichever faith appeals to them.