The preposition de is not mandatory but idiomatic here.

À tous is there to make clear who leur refers to, i.e. to make clear everyone belonging to the group referred to is at fault, not a subset.

In theory, the preposition de is used after la faute (e.g. c’est (de) la faute de Pierre) but in colloquial French à is often used instead, and this is not new:

Je suis tombé par terre,
C’est la faute à Voltaire,
Le nez dans le ruisseau,
C’est la faute à Rousseau.

Les Misérables, Victor Hugo.

In fact c’est de leur faute de tous would be not idiomatic at all because the de in “de leur faute” is colloquial while the de is “de tous” is formal. The literary/formal variant is “c’est la faute de tous.“

The suggested form c’est tout leur faute is colloquial and has a different meaning: “Everything is their fault”.