I've noticed that medikits are extremely effective, while the hospitals don't seem to be working. Even when they are working in a future release, if the soldiers heal at the rate of XCOM Apoc, the hospital will still be overshadowed by the miraculous medikits.
My idea is to give hospitals more of a use.
Medikits should be assembled by medics in the hospital, the way most things are produced by the workshop. They could have 5 uses before needing replenishment/replacement, and an improved model can hold twice as much, and could act as a sedative to boost the morale of a panicked soldier. Heck, you could even throw in stimpacks to temporarily boost strength and speed (though these could be in a different package from the medikit).
You may consider allowing the assigning of a medic to come on missions; they could require fewer TUs than a soldier to apply medical aid.
You may also consider medical procedures to implant advanced equipment in a soldier's body, like grafted body armour or cybernetic implants which need have no game effect more than permanently boost a soldier's stats. These procedures would be unrecoverable expenses when the soldier dies, unlike standard issue equipment.