My mum was like this some years ago, earlier in her dementia journey. I had to instruct her carers only to give her water and meds, no food or hot drinks, in bed. If she could trick them by pretending to have a headache she could spin it out all day, but if she needed to get up to have her food then she was more motivated to get up!
The other thing the carers could do was to give her plenty of fluids, so that she would need to get up to go to the toilet. Then when she came back they would stand in front of the bed, blocking her access, and say brightly "Oh good, you're up now, let's get you dressed." If that didn't work, then on her next toilet trip they would strip all the bedding off so that the bed no longer looked like a cosy haven.
It's all very well to say "Ah, bless, why shouldn't they stay in bed?" Well the answer is that it seriously shortens their lifespan if you let it become a habit. People need to move about to keep their lungs and general circulation healthy. They need to use their muscles. It doesn't take long for an elderly person's muscles to weaken through inactivity and then they can't mobilise even if they want to. They will also be at greater risk of falls. An immobile person in bed will develop pressure sores and is at risk of developing pneumonia because fluid builds up on their lungs.
It really isn't good for someone to take to their bed before nature puts them there, to be blunt. Nobody would begrudge them the odd duvet day. The trouble is, in my experience, that the person with dementia cannot remember that they've been indulged as a treat and will just make the same demands every day. Once they succeed in making it a habit you've the d*v*l's own job to restore a healthier daily routine.