Even cats will walk on a leash if you train them right.
Yeah, see: https://www.youtube.com/watch?v=yyeKQuB_YzE
Bigger breeds like savanas, toygers, or bengals need to be exercised if one doesn't have a large enough house space or room for a partnering cat. They can be leashed and walked with a little training. Some people might have bright enough cats to stay within walking distance, but these bigger ones will bounce around like a pinball at the sight of the outdoors.