1-Very few mages can heal people properly
Perhaps the number of magic-users that can fully heal people of serious injuries are few and far between and only to be found at the Archmage level. Low-level magical healing can be done by any competent magic-user who knows the right spells, and serious wounds can be healed temporarily by magic, but unless the magic-user is excessively powerful, it is just a matter of time before the wound painfully and perhaps fatally cracks open again.
2-It costs HOW MUCH?
The Healer Mages of both genders are organized into a single, country-wide or even planet-wide Healer's Guild, a de facto cartel, and if the adventurers don't have health insurance and/or a great deal of money, the price for healing any serious wound through healing is astronomically expensive.
3-It opens the body to possession
Healing someone by magic has the unfortunate side effect of disrupting the body's internal firewall against ghostly or demonic possession, making the healed person vulnerable to such takeover effects for the rest of their lives. If ghosts are common, most people would hesitate to put themselves in a position where their bodies can be taken over.
4-One person's healed wound is another person's OWCH!
When a wound is healed by magic it is merely transferred to somebody nearby, who might even turn out to be the healer. Most civilized places ban healing spells as a result. As well as a legal ban someone wounded by someone else's magical healing might gather their friends to attack the healer responsible, the adventurers or both, or heal themselves by magic injuring someone else in the process.
On a critical failure, the magic cases the healed area to animate and in effect refuse to do what the person's mind is telling it to do. The area can still be felt but can't be controlled. If it is the mind that has been healed, the person in effect becomes someone else entirely.
6-It can be unhealed
A wound healed by a mage user can be unhealed just as quickly by the same magic user, and whilst it's illegal to do this and most magic users are not that malicious, a minority of healers will blackmail the healed one either by themselves or as part of the world's equvilent of the Mafia. Toughs will stab someone, a healer will heal him or her, and then demand a certain amount of money a week not to cancel the healing and reopen the wound. Even if the person flees or goes into formal witness protection, the wound can still be reopened at any time just by the healer cancelling the spell.
7-Upon death, a magically healed person will rise as a zombie
When the healed person later dies be it of a wound, disease or just getting very old, the body will very quickly rise as a zombie unless it is cremated within minites, and if not controlled by a magic user or cut down, will wonder around attacking the living and generally making a nuisance of itself.
Additional Ideas (1)
The impression I'm getting from this is that the author is assuming a bit too much. Speaking in general, the problem I see with using magic to heal is that it can use up a resource in short supply. Or, it may not work as well or as swiftly as one may think.