As I mentioned in a sister comment, Gödel's incompleteness theorems also throw a wrench into things, because you will be able to construct logically consistent "truths" that may not actually exist in reality. At which point, your model of reality becomes decreasingly useful.
At the end of the day, all theory must be empirically verified, and contextually useful reasoning simply cannot develop in a vacuum.
Those theorems are only relevant if "reasoning" is taken to its logical extreme (no pun intended). If reasoning is developed/trained/evolved purely in order to be useful and not pushed beyond practical applications, the question of "what might happen with arbitrarily long proofs" doesn't even come up.
On the contrary, when reasoning about the real world, one must reason starting from assumptions that are uncertain (at best) or even "clearly wrong but still probably useful for this particular question" (at worst). Any long and logic-heavy proof would make the results highly dubious.
At the end of the day, all theory must be empirically verified, and contextually useful reasoning simply cannot develop in a vacuum.