My grandmother is eating much healthier now that she's in a nursing home versus her own home. Many elderly people stop cooking healthy homemade foods for themselves and start eating microwave or TV dinners, crackers or other snack food. For these folks, just eating regular meals again with some meat and veggies is a huge improvement. My grandma now has to have a pureed diet and she eats pureed meats, veggies and fruits (they don't puree breads) with diabetic low sugar icecream for desert. Probably the best diet she's had in 10 years. And she is getting stronger and clearer-headed with many more lucent, good days. It's fabulous to see.
So, yes. The elderly can definitely improve even pretty severe dementia with improved nutrition. But I doubt it would be practical or even a good idea to remove all bread or beans, since most of the residents have spent 90+ years having a piece of bread with dinner. They would probably be upset and angry at the change and that type of stress isn't any better for them than the roll. My great aunt (grandma's sister) is in the same nursing home and the staff would pay miserably if they took her bread away. She has quite a temper and would be really upset at that type of change. And she wouldn't understand it either. A better approach would be to just get them to eat more of the good foods so they don't eat as much of the bad ones (an approach many paleo parents use with toddlers). My aunt has noticed the change in my grandma and she is sure it's because my grandma is now eating vegetables again. She gets that part and actively encourages my grandma to finish her meat and veggies at dinner.