Would the same thing be true of men with low T, who have been prescribed Testosterone Supplement for the rest of their lives? If this is not know now, it is likely to soon be investigated.
No! If T caused dementia (or prostate cancer, etc.), teenage boys would get it. The risk is with synthetic female hormones, and even that risk is exaggerated.
Testosterone restoration is excellent for quality of life and general health. The main risk with T replacement is that doctors will not prescribe enough to restore youthful levels. The significant negative side effect is potential for increased body hair and increased hair loss in men genetically predisposed to have male pattern baldness. Risk of hair loss (for a minority of men) is worth it, in my opinion, and it can be managed with hair replacement surgery if it bothers someone enough.
There may be risk if T is used in someone with active prostate cancer, but in that case, doctors will not prescribe it for fear of malpractice. Experts in T replacement might still prescribe it cautiously.