Steelmanning their argument, employers will see benefits because while the employee might be more productive than with an LLM in the first two hours of the day, the cognitive load reduces their productivity as the day goes on. If employees are able to function at a higher level for longer during their day with an LLM, that should benefit the employer.
Except the causes of burnout have almost nothing to do with the type of cognitive load associated with coding, debugging, etc.
https://www.mayoclinic.org/healthy-lifestyle/adult-health/in...
Of the six general causes listed, four are institutional or social, having to do more with the workplace or coworkers: lack of control, lack of clarity, interpersonal conflicts, lack of support. IME, in tech, these are far more common causes and more deeply tied to the root of the issue than specifics of work.
The remaining two are productivity-related issues: too much/little to do, problems with WLB.
I would note these are tied into lack of control/clarity/support, and conflict. In a healthy work environment, expectations should be clear and at least somewhat flexible depending on employee feedback, and adequate support should be provided by the employer.
That aside, it's unclear, and I would argue unlikely, that AI-related productivity gains will help with workload issues. If you do disproportionately more work in an overworked team/org, you will simply be given more work. If many people see gains in productivity, then either the bar for productivity goes up, or there's layoffs. Even if you manage to squeak by / quiet quit with much reduced cognitive load for coding, and that's most of your job, unless you are fully remote the most likely change is your butt-in-seat time will go from "mentally taxing coding" to "mentally toxic doomscrolling."
I think we are all working without data here, it's all conjecture.
I went with OP's hypothesis that you are not faster, you throw things at the wall, wait, and see if it sticks, or re-throw it until it does. This reduces your cognitive load, but might not actually make you more productive.
I'm assuming here that "you are not more productive" already accounted for what you are saying. Like in a 8h day, without AI, you get X done, and with AI you also get X done, likely because during the peak productivity hours of your day you get more done without AI, but when you are mentally tired you get less done, and it evens out with a full day of AI work.
There's no data here, it's all just people's intuition and impression, not actually measuring their productivity in any quantifiable way.
What you hypothesize could also be true, it the mental load is reduced, can you sustain a higher productivity for longer? We don't know, maybe.