They already do this, listen to the radio at off hours and there will be many job ads with instructions to apply via postal mail. Of course the reason isn't to deter LLMs it's to deter Americans so the employer can claim no Americans applied in their visa and green card filings.
Do FAANG, FAANG wannabes, or startups do this for software development roles? I've never heard of that.
As much hate as H1Bs get, I’ve worked at two large companies where the publicly posted salary range for H1B applications were consistently higher than my own. In all humility, I was more qualified and more experienced than required by the position.
Maybe there is a dearth of talent, maybe it’s about control, maybe is someone trying to get a friend hired. I don’t think it’s about the money.