For real aerodynamics the tyre plus rim would need to be 4 times deeper than it is wide so depth of rim would need to be factored in for anyone really worried about it.
Not strictly true. Even a brick has aerodynamic properties and you can improve these properties in small and meaningful ways.
Back to tyres... you can virtually disregard the rim for most rim (e.g. non-aero) rim sections. The main aerodynamic effect is then that of a bluff body, being the tyre. Make the tyre wider, you increase the drag, simple as that.
Not strictly true. Even a brick has aerodynamic properties and you can improve these properties in small and meaningful ways.
Back to tyres... you can virtually disregard the rim for most rim (e.g. non-aero) rim sections. The main aerodynamic effect is then that of a bluff body, being the tyre. Make the tyre wider, you increase the drag, simple as that.