I think the best answer is to look at the safety issues. Does the person have enough safety awareness to be up and about on a walker by him/herself? Or is a fall and a broken hip waiting to happen?
My husband has vascular dementia, he needs a walker for balance, but he is very impulsive and will start walking much too fast and not paying attention to where he’s going. His PT did not recommend a rollater as it would encourage him to wheel faster and faster. Also not recommended were the “ski-style skids” on the back legs of his walker (same issue with speed).
Due to his lack of safety insight and impulsiveness, what was recommended was a wheelchair with an “anti-rollback” device. I ordered both online from Walmart, and hired a Fix-it guy to attach the device to the wheelchair. When my husband stands up, the wheelchair stays put- he would never think to apply the brakes. He uses foot propulsion to buzz around the facility safely, is up and down independently for toileting, in/out bed, on/off his easy chair. I take him for walks when I visit, but I walk in front of him so he can’t speed up with the walker. Staff walks with him regularly too.
As the dementia progresses, you do find yourself needing to calculate the “least harm” with decisions needing to be made.