1. "Bogus religions"
2. "Good of Logic"
3. Has a picture of the Bible being marked as wrong.
Every human thought process tries (and fails) to be logical - as in, based on certain evidence. The authentication of that evidence is up to you. If you're talking about "bogus" religions like classical Greek/Roman beliefs - sure. Those have enough evidence against them to sufficiently express disbelief.
But MAJOR ones like the classical triad of Abrahamic faiths? Absolutely not. Too much people in favor of it, too much evidence that supports their beliefs, and too much controversy. And BTW, logic has no separation from beliefs - and considering the secular nature of science today anyway, religion does not in practice end up restricting anything. Your so-called "bogus" religions WERE responsible for a few things like algebra, astronomy, physics, (hint: all of science) -> just to name a few :)
I should not have to argue the existence of good and evil, since that is a different question. But I am building off of the conclusion that they do.
I should not have to argue that religions involving morality (which is most of them) that value goodness in seemingly various definitions, are bogus because of so. This very question uses a definition of good, or positive, and to disband the definition of 'good' would be counter-productive to what is suggested. --"for the good of logic".
Like Alphamus says before me, religions laid the foundation of the world as we know it. Without them we wouldn't be as advanced with at least our sciences today.
Can they be "scrapped"? No. At least, you'd probably have a better chance to kill of an entire human race, than destroy almost all religious organizations. And permanently so to add on top of it? This is a very silly question.
This question assumes that that would be for the "good of logic", but as one should find, logic not only lays it's foundation on religions but is pushed further by it.