If someone who contributed to the Linux kernel has their resume on par with a spammer who lied about it how do we know who is correct unless there is a verification system?
Put simply, organizations needing skilled personnel can delegate post-application screening to their set of approved staffing firms. Said organizations can employ initial screening techniques to filter out obvious fraud, such as requiring online applicants prove they possess the email/cell phone provided via industry standard mechanisms (while employing deny-lists as applicable). Given the remuneration commitment each hire represents year-over-year and the ability to hold staffing firms accountable, their fees are typically quite reasonable.
Why you introduced the question "what impact have LLMs had on productivity?" in this context escapes me.
When the problem definition is "companies want applicants who are known to be humans having a minimally vetted work history", Occam's Razor[0] implies people can do so efficiently. If for no other reason than it being trivial for one person to converse with another.
How would the above result in:
... of course a reduction in industrial productivity and a
negative contribution to economic growth.