The bottom line of this discussion is that, because of who God is and what Jesus Christ has done in dying for us, changing the throne of judgment into a throne of grace, we who trust Christ are to draw near the throne of grace in confidence. If we came in our own merit, we could have no confidence at all. The throne of God would be a place of terror. But since God has done what was needed to take away all judgment for our sin, it is now sin for us to come in any other way but with confidence.
Why is the throne of God described in Hebrews as a throne of grace? The answer is obvious. It is because God is a God of grace. Indeed, he is the God of all grace. It is only in God that true grace may be found.