Whole spices are suggested because they retain their flavor much longer, and thus tend to have richer flavors, even if they are not fully extracted. The reason for this is that they have less surface area, so volatile flavor oils do not evaporate away as easily, and other parts of the taste do not get oxidized. They are also easier to strain out of the mixture, so they don't give an overpowering flavor or leave a gritty residue.
So, yes, you are wasting some of the flavor, but in exchange you get more of the subtle flavor compounds that ground spices tend to lose. Note also that steeping in milk will extract considerably more of the flavor from whole spices, because a lot of the smell and taste comes from chemicals that are more soluble in fat than water.
As another option, instant chai blends dissolve completely, but tend to lack the more subtle flavors of the spices.