Things like this are easy to say when you're the employer, you get to select whatever portion of resumes you want with impunity. As the employee that needs a job to keep on living people tend to do anything they can to get their foot in the door. Hence, this is why resume inflation/copying known good resumes was a thing long before LLMs.

Now, if you're a smaller business, you'll very likely notice these effects and the number of resumes is rather small. But in larger businesses they may get thousands, tens of thousands of resumes, and the vast majority of them are culled by automatic processes and people that have no understanding of the real requirements of these jobs and said 'generic' resume might just allow you to get past said filter better than randomly stating who you are.