Ermmm, then why do we still use mortar? That’s a bold uninformed statement even for stw!
From Wicki (to confirm my 30 years in building):
“Bricks, stone blocks, and other masonry units are typically laid in a bed of mortar. The process of placing a masonry unit in a mortar bed causes the mortar to be extruded between units. This excess mortar is cleared and shaped before the mortar hardens. In some cases, the bedding mortar is meant to be seen and the mortar joint is immediately given a finish profile. In other cases, especially where the mortar is pigmented, the bedding mortar is removed from the joint before it hardens (usually a depth that averages about one inch), and then pointing mortar is applied in the void and shaped with a finish profile.”
So its the mortar bed which bonds the bricks, pointing or re-pointing is a decorative finish which also stops moisture from getting to the mortar bed.
Regarding the OP, I’d still rebuild that wall 🙂