On the other hand, no one to place the blame on if management does it themselves.
That's definitely not true.
There's always people for management to blame. That's the great part of being management.
By definition, there's someone/thing you're managing that you can pass the blame onto.
The recent cases of companies who deleted their prod DBs while using LLMs are blaming “the rogue AI”. So it seems you can just blame AI lab companies and folks roll with it. Even better, they asked it to generate its own apology, no need to spend time trying to explain to your customers why everything is gone