Well, most people who "blindly trust" LLMs also blindly trust Google results, Wikipedia, the first Stack Overflow answer, a friend who sounds confident, and a news headline they didn't click through. So, what do you do. As giantg2 has written in the comments, they are a little special.
I think this binary "fire vs. build better" is probably NOT the right perspective. Maybe a different perspective could be, since the cost of attempting things is falling rapidly, what features are now worth trying, that were NOT worth building because the implementation cost was too high.
I think companies that maintain the same product roadmap, will stagnate irrespective of whether they keep the engineers or fire 90% of them. The ones that will win, in my humble opinion, will be the ones that ask, "What can we build now, that we could not build before due to any reason (cost, expertise etc.)?" That is an entirely different question.
At the same time I would recommend, document your methodology explicitly in the dissertation, describe the verification pipeline, and make it clear what you reviewed manually versus what was automated. That transparency converts "dishonest?" into "methodologically rigorous."
Here is the thing, academic policy is NOT really about honesty. It is about trust. Universities cannot distinguish your workflow from someone who prompted GPT to write their lit review wholesale.
More than the ethical distinction, I believe the rule around AI usage is blunt because enforcement is pretty hard.