Why are Sakura's feathers so powerful?

Question

Princess Sakura of Tsubasa Reservoir Chronicle has her memories scattered to many dimensions in the form of feathers. These feathers are incredibly powerful, able to do things such protect buildings and water underneath from acid rain. Why do the feathers have this power?

Answer 1

According here and here,

Sakura is revealed to have strange powers when she has a vision of a mysterious symbol and places she has never seen.

So,

Since these feathers represent Sakura's soul, these hold an enormous amount of magical power. Each of them affect their surroundings differently.

In the last arc we learn that the true power of those feathers are

to cross dimensions and time.