Amount of Distortion at Continental Collisions
I think of the plates not as icebergs floating around in a sea but as pieces of porridge skin on the surface of gently simmering porridge, moved about by convection forces from below.

The Indian plate became fused with the Australian plate about 43 million years ago, so now there is only one plate, the Indo-Australian plate. Since then, the whole mass has been moving north at about 4 cm per year. A relatively small amount, perhaps a quarter of what was once the Indian plate, has crumpled against the Eurasian plate to form the Himalayas.

I don't know what the total mass of the Indo-Australian plate is, but it must be many trillions of tons. Imagine the momentum of many trillions of tons of rock moving at 3 mm per month, in addition to which there are convection forces from the mantle pushing it along! Bulldozing the Himalayas must have slowed it down a little, so 43 million years ago it was moving even faster.