Fortunately I've not had to do an extension yet in my few years at Delta, but I was frequently put in that position at my dirtbag regional. A few extensions I accepted, most I didn't. I never accepted one if the FO wasn't comfortable and 100% on board with it. There were a few instances where I accepted a 30 or 60 minute extension, but not the full two hours.

The ones I didn't accept weren't because I was fatigued at that moment, it was because I know my body and I knew that I was already starting the downward slide and that I would definitely become fatigued at some point during the extension. That wouldn't be safe and I wasn't going to be put in that situation.