I like that you explicitly pointed out that flying into a mountain is not the recommended course of action for pilots.
Humor aside, this crash also includes a lot of broken down communication, so in most cases, even if TCAS fails, a crash is not inevitable. A pilot aware of the priority TCAS has will definitely communicate a failure to abide by its orders.
Specifically, the ground proximity warning (as well as the stall warning) takes precedence over TCAS. This is just fine, since the "descend" aircraft in ground proximity will level off while the other climbs. You're not likely to find a condition where neither plane can deviate because the descender gets a ground proximity warning and the ascender gets a stall warning at the same altitude, since those are typically associated with aircraft flying close to their minimum and maximum altitude, respectively. You would need to have two aircraft flying level very close to the ground, at least one of them near its stall speed, which simply is not a flying condition used by commercial airliners.