Why do we boil whole spices when making masala tea?

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.

To avoid wasting whole spices (especially cinnamon), you can reuse it for couple of times still there will be more flavor in it.

You can use ground spices if you want to. These recipes are traditional, and the people who brew them first most likely didn't consider wasting a clove or two a problem; they probably had whole bushes of the stuff growing in their back gardens.

The advantages of the whole spices are (beside the fact that they store better, which BobMcGee already mentioned) that you don't risk a cloudy tea (powder is hard to strain) and that you don't have to spend time grinding them. If you care more about using up less spices per cup than about storage and/or efficiency, and don't mind some powder left in the cup, it is OK to use ground mix. I would try using a paper tea filter for it, as it is likely to hold the powder better than a mesh strainer.

I personally use both whole spices and ground spices for making chai. It all depends on what spices you are using and the quantity. I always crush cardamom for chai to bring out the flavor. I crush or grate ginger. cinnamon and clove can be used as whole just for convenience. But imagine making tea for 10 to 20, I will just add whole spices for time saving.