I'd have to think about applying it to B/X or LotFP, but it would make combat much more deadly.
Edit: Now that I've had time to think it's really infected my brain. I can't shake the idea that it would really make combat quick, but require more tactics on both the part of the DM and PCs.
ENCOUNTER REACTION CHECKS: I'm a big fan, and making combat more deadly will increase the likelihood players will want to at least try to talk first. Of course, this puts more pressure on the DM to come up with what monsters, NPCs, and adversaries want from the PCs (which might improve adventures as a whole).
INITIATIVE- Becomes extremely important to keep and maintain this in combat because of a single hit yielding so much damage. Maybe light weapons increase the initiative die size?
RANGE- Another factor that increases in importance. In most D&D combat ranged weapons are "meh" because most combat does not take place on a wide enough battlefield. However, if a bow gets you 1 or 2 attacks without any response that's huge in this system.
MELEE- I would still want to try to give other properties to weapons beyond to-hit/dmg. Big weapons are already going to hit hard with 10 or 12 damage. Maybe add reach, parry, slow, reload to emphasize other combat aspects. Weapon choice should be distinct and easy to understand with different weapons giving different situational advantages.
COVER- need more of it on the table to help increase AC especially for those characters with armor restrictions.
MORALE CHECKS- like REACTION CHECKS above, I think this optional rule is strengthened when combat is made deadlier. Now its easier to perform a first strike, kill a leader, or 50% of the force, so it makes sense to force the conflict into a route or non-combat exchange.