Cannot say about layoffs in the past, but at the FAANG I am at, the most recent layoffs were absolutely random on the individual level, but not as random on the organizational level in my org.

E.g., "this group of 4 engineering teams responsible for area ABC needs to get cut by 30%, because we are deprioritizing this area"? and then the actual people who get laid off from that group of 4 teams are chosen entirely randomly. It perfectly aligns with the idea that the layoffs are mostly due to major changes in prioritization of projects (due to recession and all), not to just cut "bad engineers." If you are ok with your company's engineering quality overall and just want to cut projects you consider wasteful or deprioritize them to save money, personal-level randomization run against a deprioritized group makes sensez

I believe part of the reason is that randomizing makes it safer for the big companies legally as well, since that makes it much more difficult to successfule sue them for unjust firing or discrimination and other reasons.

Some from every column. In larger companies, firing decisions are often political decisions.

Yep, I've been in companies where it's the whole "every department needs to cut" rather than only cutting dead weight.

That's what you, as an engineer would do if you were to do layoffs starting from first principles, but that's not who's doing the layoffs.