In critical applications, much more than you'd imagine. Lots of defence and critical component suppliers still maintain a significant amount of hand work for low volume and critical areas.

Don't have a source unfortunately other than personal experience working as an engineer.

For low volume, it can cost more to set up the P&P machine, deal with alignments, check first articles, etc. than just soldering a few (dozen) board by hand. And there are a lot of small companies in niche markets whose annual production of a PC board might be in the single digits.

That and, people who hand solder stuff all day are fast.

Over the years I have seen couple of closeups of various boards on youtube. As electronics is my hobby, I tend to pay attention to this. They all looked hand soldered to me. And the soldering job always looked very, very high quality.

I've been told that in areas where lots of prototyping isgoing on, there is lots of scope for manual rework. (a pcb design only 95% correct needs modifications to figure out the right design)