You're summarizing the debate between "originalism" and "pragmatism" theories of judicial interpretation. The former looks at what people supposedly intended and confines the meaning of the text to that. It's the weapon of choice of conservative justices (because of course, the Founding Fathers couldn't intend to give marriage equality). The latter looks at what the text does, in today's context. It's the approach preferred by progressives because it accounts for how the effects of a text can change with time (and society).

In general I would agree with you, you oughta look at what a legislation does in practice. But here, because there is a sense of urgency (sending a gay refugee back to Somalia, for instance, is akin to signing their death warrant) and because the executive order hasn't been around for a while, I think it's ok to refer to what the administration intended the order to do. Because we don't have a lot of field evidence. As we see concrete evidence for the effects of a legislation, I think you're right and the weight of what it was theoretically intended should decrease pretty quickly (and it usually does).

The administration also didn't present to the court any sort of evidence supporting the claim that it would prevent terrorism.