Rightly or wrongly, I think some people (I probably fall into this category) prefer the idea of the meat being properly cooked all the way through. I get that people will say it 'is' cooked even though it might still be a bit red/pink in the centre, it's probably a visual thing i.e. if it's brown all the way through then it's cooked through.My mates wife has to have her steak cremated. Once, when we were in a decent restaurant when on holiday, three couples all opted for the Chateaubriand. Of course, she asked for theirs to be 'well done'. The waiter looked at her like she was mad. The chef even came and checked that was what she wanted. Their one came up like a charred sole of a boot. She enjoyed it, her husband was 'disappointed'. We still laugh about it. We've had Chateaubriand a few times since when we've been out. Mrs Mottie is not a real steak lover so she has something else, Mrs charred steak has...a charred steak and me and my mate have the Chateaubriand between us! When we order it, one of us will always say to the waiter "We're not a couple!".
Before anyone starts, I'm NOT saying what I've typed is factual from a scientific pov, I'm simply stating a possible reason why some prefer their steak well done.