My problem with this is that I think a lot of the changeable minds that are on the fence will recognize how it isn't really hypocritical, and so this misses the point and just makes it look like a stupid complaint. Because indeed, there isn't hypocrisy going on here. The mentality is wrong for other reasons, but not because of hypocrisy. So when it comes to changeable minds, I feel like it's better to put forward solid reasoning rather than merely sophistic reasoning - as the second kind is usually only useful for preaching to a choir who is willing to overlook logical flaws.
I guess I should also say I totally understand that you might convert some people with a hypocrisy argument. But... Although it may be idealistic of me, I'd much rather make converts out of people through actually true lines of reasoning rather than ones that are merely compelling.