Likovod HaRav Shlit”a’,
Does the Rav allow Jews to own dogs as pets? Does he allow Jews to own pets at all, if there is no pressing need for them (i.e. they are not needed for protection or to serve as a seeing-eye dog, etc.)?
There is certainly no prohibition in owning a pet dog. Even if it is not for one of the reasons you mentioned but only for pleasure and recreation, it would be permissible to have a pet.
Whether or not it is recommendable would depend very much on the community one belongs to and to an extent his hashkafas hachaim, a very personalized question.