Primal is the only client I know that has a built in wallet, and marketing this way. Everyone else is commited, with optimism, that new models will work themselves out. 
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Current has one too. They've had it since before Nostrica.
Wisp has one built-in, but there’s no “Start in wallet” feature like Primal, and the wallet button isn’t front and center on the menu. It also has a “Fiat mode” for people who don’t think in bitcoin.