Tea in most traditions is steeped in water below boiling for a few minutes. Indian chai is boiled hard with milk and spice, and every part of that difference is deliberate.
The leaf is made for it
Most chai uses tea processed by a method that crushes and tears the leaf into small granules rather than keeping it whole. That vastly increases the surface exposed to liquid.
Such tea extracts very fast and very strongly, producing a dark, brisk liquor with pronounced astringency within a minute or two.
Steeped gently it would be harsh and thin, so the processing and the brewing method developed together rather than one being applied to the other.
Milk changes what can be extracted
Milk proteins bind to some of the astringent compounds in tea, softening the sensation on the palate. That allows a much stronger extraction than plain water would tolerate.
Fat in the milk also dissolves the spice compounds, most of which are fat-soluble and would extract poorly into water alone.
Boiling the two together therefore does two jobs at once, pulling more from the tea while making the result drinkable and carrying the spice throughout.
Spices need more than steeping
Ginger, cardamom, cinnamon and pepper release their aromatics slowly from dense plant tissue, and a few minutes below boiling extracts very little.
Crushing them first and boiling them in the milk gives both the mechanical damage and the sustained heat required.
Ginger in particular benefits, since its pungent compounds transform under heat into a mellower, rounder form that tastes quite different from raw ginger.
Why sugar goes in during the boil
Sugar added while boiling dissolves fully and participates in the browning reactions taking place between milk protein and milk sugar during sustained heat.
That contributes a faintly caramelised note which is part of the character of a well-made cup and is absent if sugar is stirred in at the end.
It also raises the boiling point slightly, which marginally increases extraction, though the flavour effect matters more than the temperature one.
Why the pouring matters
Chai is traditionally poured between vessels from a height before serving, which aerates it and cools it to drinking temperature quickly.
Aeration lifts the volatile aromatics into the air above the cup, which is where a large part of what is perceived as flavour actually registers.
It also mixes the layers, since a boiled pot separates as it stands, with fat and foam rising and the heavier liquid settling below.