The Bible's comfort verses do not rush anyone. Psalm 34:18 does not say the brokenhearted will be fixed; it says the Lord is near to them. Presence first, repair later — that ordering runs through this whole set.
Comfort here is also personal: God “binds up” wounds (Psalm 147:3) the way someone tends an injury by hand, and Revelation's ending has Him wiping tears away Himself. These are not distant sentiments; they are descriptions of nearness.
One honest note: if you are grieving, a verse can accompany you but cannot carry the whole weight. Let these words be a companion to — not a substitute for — people who sit with you, and professional help when the weight is crushing.