A phone's font is large. A picture let's you see code/logs properly formatted and in proper context. It also gives you the opportunity to circle/arrow and otherwise annotate the points of interest while displaying context around.
A picture prevents you from copying, but often that's not as important. One can use judgment to determine whether a picture or text can be better.
Receiving such messages can sometimes mean I need to transcribe a bit of what I'm seeing, but the added clarity to what they're trying to communicate can be worth it. I welcome it.
I don't think people are using any judgement, but if they are it is only poor judgement. I've rarely received a helpful screenshot like you describe.
I tend to get things like 1/3 of a terminal window missing all of the context. No commands and only half of the error.
Ever receive a photo (not a screenshot) of a spreadsheet when they expect you to do something with the content? I have.
Another personal favourite is a browser window cropped so tight I can't tell where they are. No address bar, page header removed, sidebar missing, etc.
Send text as text! One of these times I am going to print the photo, annotate it, and fax it back. Or maybe I need better coworkers.