[yummyfajitas]

The benefit of the models is that they force you to both explicitly state all your assumptions and also verify that your conclusions logically follow from your assumptions.

Further, it enables others who wish to criticize it to easily derive predictions and show that those predictions fail to match reality, while making it impossible for you to say "that isn't what I meant". If the math says it, that's what the model predicts.

Vague verbal reasoning just involves a lot of time wasting - "your model seems to show this, I think" -> "no that's totally not what I meant, you don't understand" -> etc.