Why isn’t a sincere heart enough? Why do outward deeds matter?

Because for every internal action there has to be an external action, and the value in that external action is achieved by the internal aspect. There is no sincerity without action, and no action becomes worship without sincerity.

Some say their heart is sincere, so they need not perform the outward acts like prayer. These are the people deceived by the devil.

The inner aspect of an action cannot occur without its external counterpart. A person may keep his heart earnest his whole life, yet there is no sincerity until it is joined to action; and he may perform outward acts his whole life, yet they do not become devotion until they are joined to sincerity.

Allah has created for every inner meaning an outer form. Remove the outer, and the inner becomes impossible; if the inner aspect of faith becomes weak, the outward form of worship becomes soulless. [Keller, Sea without Shore]