You're absolutely right to completely ignore what the Fifteenth Amendment doesn't say.
it specifically says that states shall not use race as a criterion in awarding the franchise, and it gives Congress the power to make sure that they don't. It really couldn't be any clearer than that.
Now you've hit the nail right on the head. As you say, section 2 "gives Congress the power to make sure that they don't."
In connection with the adoption of the Voting Rights Act, Congress held lengthy hearings and made the factual determination that some states were using literacy tests for the purpose of denying and/or abridging the right of black citizens to vote and that the right of many black citizens to vote was in fact being denied and/or abridged because of that practice. Accordingly, it determined that it would be impossible to enforce the Fifteenth Amendment without suspension of the literacy tests. Given these factual determinations, Congressional legislation designed to stop an intentional violation of the Fifteenth Amendment was entirely "appropriate."
After passage of the Voting Rights Act, the black voter participation rates went up in the affected states. And before too long, even George Wallace of Alabama (who had always gone out of his way to cast himself as the Babe Ruth of segrationists) evolved into a valuable political friend of the black community.
Not to sound heartless or anything, but so the hell what? You acknowledged at the beginning of your post that it was appropriate to ignore what the 15th amendment doesn't say, and it doesn't say that the states can't have impure motives when instituting suffrage criteria - it only says that they can't use that one particular criterion. Under what third-world conception of law do the authorities have the power to take action based on someone's reasons for doing what would otherwise be perfectly legal?
Accordingly, it determined that it would be impossible to enforce the Fifteenth Amendment without suspension of the literacy tests.
Then they were totally disconnected from reality. The literacy tests did not in any way interfere with Congress' ability to prevent racial tests from being instituted, which under the 15th, was the only thing they were allowed to even concern themselves with.