It doesn't even do that. It restricts what kind of laws congress can create, not the reasoning congressmen use when choosing which laws to support. Completely

It doesn't even do that. It restricts what kind of laws congress can create, not the reasoning congressmen use when choosing which laws to support. Completely secular and constitutional laws may be enacted by congressmen that have religious reasons to support that law; e.g. religious legislator may vote for a law against murder because murder is against their religion. The first amendment doesn't regulate the thoughts and reasoning of legislators; religious reasoning for secular laws are fine. And conversely, secular reasoning for religious laws doesn't make the law okay; a cynical atheist might say that religion is necessary for controlling the unwashed masses, but despite that secular reasoning, a law mandating a religion would still plainly violate the first amendment.