"Delayed" typically gets put up automatically when the Expected time is increasing by one minute every minute, i.e. the train is stationary. It is I guess a response to people saying that was ridiculous.
When the system was implimented, the "Delayed" trigger was at 5 minutes of no movement.
At a later date, it was reduced to 3 minutes as requested by Arriva Trains Wales (if I remember correctly!) and no other TOC was against the change. No source, but I was at the very same meeting when the change was implimented.
It also transpired different people around the country prefer different things.
Some don't mind it showing "Delayed", others prefer an increasing delay time.
The problem comes in where if you estimate a delay time, say 15 minutes, then the problem is fixed much sooner (so only 5 minutes of delay), some customers may have left the station to get a sandwich and then may miss their train.
The only way to solve that problem is by using "Delayed" - which then causes "by how long?" questions. The road usually leads to a bit of frustration when the answer is "Don't know" - yet on a motorway, people are accepting a long delay has no time frame.
I question why the railway has to define a delay period, yet a motorway does not.