You are absolutely correct. Until society recognises dementia above and beyond "management " or as simply an 'old age' phenomenon, things will not change. Cancers, heart disease, strokes et al are mostly perceived in the light of understanding and subsequent cure and care by default. Caring in the world of dementia goes unsung generally owing to the misconceptions. The stuff of bemused quips and quaint commentary, the reality is completely and utterly different as you will know. And yes, Carers have precisely the same rights as any other human being whoever they are or wherever they might be.
Like a mother with her newly born child, the act of caring and protection is a deeply meaningful act, ancient in its nature and in its need for survival. You don't need to open a book to be aware of that instinctive humanity. With dementia the one living with the disease is that newly born child - vulnerable and innocent - and one cares and protects without reservation. But you have only so much energy, so much time, so much ability at your disposal. Thus one needs respite and support. That is profoundly true and absolutely essential. Support one will find here and from varied and often extraordinary people who have cared and are caring over and above recognised and accepted levels of Care. As to respite? You cite that predicament very clearly. Meantime one carries on because one has to. Because we are human. Therein lies the 'problem'. Reminding the world of that salient truth?
Warmest wishes.