Why does sunset towers only have a few tenants?

Sunset Towers has most of Mr. Samuel Westing's heirs, he had sixteen. Barney Northrup invited most of them to come live at Sunset Towers. Although Barney is said not to actually exist. Barney is really Windy Windkloppel, who has four identities - Sandy McSouthers, Barney Northrup, Julian R. Eastman, and Samuel W. Westing.