Those soldiers would be formidable, but not as the whole army, but rather a part of an army.

If I understand correctly, "Soulless" are comparable to ASoIaF/GoT "Unsullied", but should be inferior to the latter because they totally lack the initiative and entirely don't feel pain rather than are able to tolerate it to the highest extent.

Other answers already pointed to the flaws of such an army. That's why I think these "Soulless" should be a specialized tool, not an all-purpose tool. You won't use diamond glass cutter to hammer nails, and, conversely, won't use hammer to cut glass. "Soulless" troops should be invaluable when you need to rout an enemy's strong point, or make "last stand". They will suffer, for sure, but would be more effective than regular soldiers. Also, the psychological factor of deploying your fearless troops should demoralize your enemy.

For most other army uses (scouting, patrolling, foraging) and fighting in tactically unpredictable situations, "Soulless" would be bad, if not completely useless.

Also (addressing some of the concerns), they must be able to care for themselves, detecting and treating minor wounds and sores. Otherwise any march, even without a battle, would deplete their ranks.