All Powers in The Contract must fit the concept of their Contractor, but healing Powers are especially restricted.
Healing Powers are for Healers
Healing Powers (Powers built out of Heal Wound, Heal Scars, and Cleanse) are restricted to Contractors who are "healers." This includes, but is not limited to, western doctors, surgeons, chiropractors, prophets, saints, naturalists, witch doctors, voodoo priests, psychic surgeons, health gurus, traditional Chinese medicine practitioners, "white mages," emergency medical holograms, etc.
These restrictions are loosened somewhat for Seasoned and Veteran Contractors, but if healing isn't a PRIMARY component of your Novice Contractor's concept, they cannot receive healing Powers.
In short, to support The Contract's Design Philosophy.
It Keeps Combat Scary
The Contract is designed to put an emphasis on outside-the-box problem solving rather than resource-management and stat optimization. To force Players to think creatively instead of just running in guns blazing, Combat must have high stakes. Death is a great consequence for poorly-thought-out Combats, but it's rather harsh. Battle scars and Injuries are consequences that doesn't involve ripping up a Character sheet. If healing Powers become too widespread, their impact is dramatically reduced. Combats are then at risk of becoming routine, low-stakes brawls peppered with the occasional, frustrating Contractor death.
"Resetting" after every Combat leads to undesirable gameplay cycles where Combat is the primary event of the game. It leads to encounters that are static and carefully tuned. The Contract is not designed to support such Gameplay. Everything from the Powers System to the Dice is tuned toward high-stakes Combat and abstract problem solving. If you play The Contract as a combat-only game, you will probably be disappointed by the lack of combat-focused advancement options, stat optimization, and encounter varieties.
It Keeps Contractors Unique
Restricting Healing Powers to "healers" may seem like it would reduce the variety seen in Contractors, but in fact the opposite is true. Healing Powers are in uniquely high demand, and almost every Contractor would benefit from having them. If every Contractor was allowed to have healing Powers, every Contractor would. That leads to homogenous, boring Contractors that spend their Gifts on the same sorts of Powers instead of branching out to explore their own individual concepts.
It Makes Healers Awesome
Support classes in RPGs often suck to play. This is because rather than driving unique action, they enforce assumed gameplay patterns or offer boring numerical buffs. Restricting healing Powers makes those who have them incredibly valuable. It gives healers immense leverage and clout amongst their peers.
In The Contract, healers often lead factions of Contractors, trade treatment for favors, and get away with things that no one else could. Principled Contractors are less likely to turn on healers than others, which enriches and complicates inter-contractor social dynamics.