There are some homes with private chapels. I imagine this was once pretty common among European aristocrats who wanted to go to Mass, but didn’t want to be around other people during it. Now, it isn’t as common anymore- although I am sure there are some very wealthy people in this country with private chapels, as well as retired priests, and priests who for whatever reason do not live in the rectory of the parish they are assigned to.
You have to have permission of the local Bishop to reserve the Blessed Sacrament somewhere. I’m sure if a private home was secure enough, and whoever lived in the home was a faithful Catholic who couldn’t go to a public church (perhaps for security reasons, or if the person living there was a retired priest- especially one who could no longer celebrate Mass publicly), the bishop would probably allow this. You CANNOT do this without permission though.
You’re absolutely correct, it’s up to the local ordinary per Canon law:
*THE RESERVATION AND VENERATION OF THE MOST HOLY EUCHARIST
Can. 934 §1. The Most Holy Eucharist:
2/ can be reserved in the chapel of the bishop and, with the permission of the local ordinary, in other churches, oratories, and chapels.
§2. In sacred places where the Most Holy Eucharist is reserved, there must always be someone responsible for it and, insofar as possible, a priest is to celebrate Mass there at least twice a month.
Can. 941 §1. In churches or oratories where it is permitted to reserve the Most Holy Eucharist, there can be expositions with the pyx or the monstrance; the norms prescribed in the liturgical books are to be observed.*
In my diocese, every rectory is encouraged to have its own private chapel for the priests to pray in front of the Blessed Sacrament in semi-private. This is by direction of the bishop.
A retired priest in our diocese who is also a caregiver requested that he be allowed to reserve the Blessed Sacrament at his home chapel because he could rarely leave due to his care taking duties. He was granted express approval by the bishop.
In another case there is a large private chapel on a large private ranch here locally. On Sundays the ranch employees attend Mass there. I think they also have one or more communion services during the week. The bishop has granted the owner of that chapel permission as well to reverse the Blessed Sacrament in the tabernacle of that private chapel.
I’d bet the Kennedy Family (as just one example) has permission from their archbishop to reserve the Blessed Sacrament in the chapel of their compound in Hyannis Port.
It’s not common, but it most certainly is possible.