Strikes a nerve, huh.
There are, of course, ready-prepared LDS answers to such common questions, but I don't think you're asking because you really want to hear those answers. If you are, you can hear about people undergoing a test on earth, etc.
The same questions apply to generic Christianity also of course, and I wrote a
post on another thread that applies here too. Just substitute "the LDS Church" for "Christianity" and "200 years" for "2000 years" (though of course many of the LDS answers are the same as generic Christian answers).
The obvious
real answer is because there is no God and therefore any religion which is going to survive, will need to come up with excuses why their god is powerful enough to worship yet doesn't appear to have any real influence on anything.
I'd guess that the chance of your questions suddenly giving a faithful believer an epiphany and inspiring them to give up their faith, are about the same as the chance of a Mormon converting you by providing sufficiently good answers.
That puts the whole game into perspective.
So the question-and-answer session is a game like kids asking about Santa Claus, as in the post I linked, with almost zero chance that the parents will suddenly say, "Yeah, you stumped me with that one. You're right, there is no Santa Claus."
The question then is, why play it? I suppose for the benefit of lurkers who might be on the fence about their belief. Or for the fun of matching wits--I used to do that with my parents about Santa, even when I knew he wasn't real, and it's still fun to do with religious people who like to play the game. Of just because "somebody's wrong on the internet," like the cartoon says.
I read the Mormonthink article on the first vision and didn't see anything there particularly stunning. Most LDS members, like other Christians, don't study their stories in that kind of detail, because they simply don't care. I'm guessing that the few who do, would already be aware of those sources. The problem is multiplied because Mormonism is so recent, so more records survive, but even other Christians have to deal with all the Biblical contradictions in the various gospels, plus all the extra-Biblical stuff that comes from Milton but has entered popular belief, the apocrypha that
aren't included...
I'm guessing that far more people give up a religion because they no longer have an emotional need for it, than because someone pointed out a logical contradiction.