It depends on the care required. If it is simply that you have an elderly parent/grandparent that doesn’t require must assistance for example, can get around on their own, but might need a little help it is quite different than one that is bedridden and needs assistance 24/7. I’ve indirectly have seen both.
Also, in the US – having in home care is like you mentioned is extremely expensive in the US. My grandmother lived with my parents for a while after having a fall. However, once the care got beyond above, where she needed greater care, lifting, helping showering, even cleaning after having accidents. It was way too much and too difficult a burden. It is much more difficult to care for a grown adult that needs all the care of infant than an infant and many people just cannot physically or mentally handle it.
It isn’t lack of love – my mom went to visit daily when my grandmother was then moved to a nursing home. She was physically unable to care for the level of care she required and was unable to financially support in home care. Unfortunately my grandmother would be covered for care in a nursing home but not in home care.