My hunch is that the evolution was driven by executives, probably in the 70s and 80s, that didn’t want to say they were firing people in order to make more money.
In other words the same dynamic that now leads to ‘impacted’.
Some members of my family (back in the day) used to be laid off from positions seasonally, and were then rehired the next year.
I suspect that in its early versions, it referred more to the notion that "we won't have any more work until the spring, so we'll see you then."
I don't know its etymology or when it might have been coopted by employers who didn't intend to rehire, but I suspect its intent is to signal that there's no ill will between the employer and the employee, and that it WOULD rehire those impacted persons in the future.
I'm not as sure that it means anything so specific now.
Manufacturing can still work like this (and maybe other industries?). You're laid off every now and then, if work slows down, but with the expectation (possibly contractually—many of these have unions) that you'll be brought back when work picks back up. AFAIK they can collect unemployment during the lay-off, so it's better than being kept on with much-reduced hours.
In the UK they have the term "redundancy" (as in "your position has been made redundant"). Can't see that term catching on in the US but it does cover the use of "laid off" to mean "the company chose to eliminate the position I worked in rather than choosing to get rid of me as a person", and thus may carry less stigma.
In other words the same dynamic that now leads to ‘impacted’.