Having carers 24 hrs can cost more than a care home and the responsibility is still on the family . Every time a problem occurs they’ll contact you to deal with it. On top of carers wages you still have to run the home- heat, light, food, repairs, council tax etc
The care home looks after them 24hrs and the problems are then removed to a great extent. Also, residents get great healthcare in a home whereas at home it’s up to you to arrange. My dad’s care home has Dr on call (& visiting every week for one am), chiropodist, hairdresser, dentist & optician, & a physio(once a week) care homes also provide entertainment & nice events so residents are not lonely or bored.
The burden of home care is huge - sounds better but in my opinion isn’t - fit the reasons above.