I think you are overlooking 4e and warlords. Lots of non-wound hp healing power narrative descriptions that fit the 4e definition of hit points.
Hit points (hp) measure your ability to stand up to punishment, turn deadly strikes into glancing blows, and stay on your feet throughout a battle. Hit points represent more than physical endurance. They represent your character’s skill, luck, and resolve—all the factors that combine to help you stay alive in a combat situation.
Using the inspiring word power, warlords can grant their comrades additional resilience with nothing more than a shout of encouragement.
Healing: Powers that restore hit points.
Level 2 Utility Exploits
Aid the Injured Warlord Utility 2
Your presence is both a comfort and an inspiration.
Encounter ✦ Healing, Martial
Standard Action Melee touch
Target: You or one adjacent ally
Effect: The target can spend a healing surge.
Level 5 Daily Exploits
Stand the Fallen Warlord Attack 5
You will not be denied victory! A determined strike lifts the spirits of your beleaguered allies and restores their fighting spirit.
Daily ✦ Healing, Martial,Weapon
Standard Action Melee weapon
Target: One creature
Attack: Strength vs. AC
Hit: 3[W] + Strength modifier damage.
Effect: Each ally within 10 squares can spend a healing surge and regains additional hit points equal to your Charisma modifier.
Stand Tough Warlord Utility 6
You fortify your allies with a few words of encouragement.
Daily ✦ Healing, Martial
Minor Action Close burst 5
Targets: You and each ally in burst
Effect: The targets regain hit points equal to 10 + your Charisma modifier.
Lion’s Roar Warlord Attack 7
With a bloodcurdling roar, you swing your weapon in a wide, sweeping arc that breaks through your enemy’s defenses. The blow reinvigorates you or one of your allies in need.
Encounter ✦ Healing, Martial, Weapon
Standard Action Melee weapon
Target: One creature
Attack: Strength vs. AC
Hit: 2[W] + Strength modifier damage.
Effect: You or one ally within 5 squares of you can spend a healing surge.
Inspiring Presence: Your ally (but not you) gains additional hit points equal to your Charisma modifier.
Defensive Rally Warlord Utility 10
You marshal your comrades and provide instructions to help them prevail.
Daily ✦ Healing, Martial
Standard Action Close burst 5
Target: Each ally in burst
Effect: Each target can spend a healing surge and make a saving throw against any single effect that a save can end. In addition, all targets gain a +2 power bonus to all defenses until the end of your next turn.
Even clerics have some healing that is consistent with inspiration instead of mending wounds.
Using the healing word power, clerics can grant their comrades additional resilience with nothing more than a short prayer.
Level 6 Utility Prayers
Bastion of Health Cleric Utility 6
You invoke a prayer that instantly fortifies one of your allies.
Encounter ✦ Divine, Healing
Minor Action Ranged 10
Target: You or one ally
Effect: The target can spend a healing surge. Add your Charisma modifier to the hit points regained.
Strengthen the Faithful Cleric Attack 7
You utter a solemn prayer as you bring your weapon down upon your foe, invoking the power of your deity to physically bolster you and nearby allies.
Encounter ✦ Divine, Healing,Weapon
Standard Action Melee weapon
Target: One creature
Attack: Strength vs. AC
Hit: 2[W] + Strength modifier damage, and you and each ally adjacent to the target can spend a healing surge. Add your Charisma modifier to the hit points regained.
Divine Power Cleric Attack 9
You swing your weapon in a wide arc around you, creating a halo of divine energy that drives foes back while fortifying you and your allies.
Daily ✦ Divine, Healing, Radiant, Weapon
Standard Action Close burst 2
Target: Each enemy in burst you can see
Attack: Strength vs. Fortitude
Hit: 2[W] + Strength modifier radiant damage, and you push the target 1 square.
Effect: Until the end of the encounter, you gain regeneration 5, and you and each ally within the burst gain a +2 power bonus to AC.