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I think it's possible to arrive at the conclusions with careful verbal reasoning, but what I'd say writing down the model does is that it forces you to confront the precision.
A bit easier to get away with hand-wavy arguments that sound correct but aren't precise about assumptions when using verbal reasoning.
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meeeh. Maybe it helps (for some) for tractability and seriously/clearly stating your position. Per Taleb, it's easier to macrobullshit than microbullshit... but I think you can get there quite easily by simple middle-school type verbal reasoning too. (After all, Austrian econ training is all about that; no need for fancy PhDs to get the point)