I have never had a problem with clerics healing during combat, but I have had a MASSIVE issue with clerics being obligated to give up spells during resting. I like that you had the option for the healing skill to be effective out of combat....Thats the ticket!
Edit : Im surprised by the number of people that voted for "It takes days, if not weeks to regain hit points by resting"...that what turns the cleric into a healbot and makes no-one want to play it.
In a system where you have to heal over time you will likely need to find a safe place to rest for the healing to be effective. in most cases that means you have to return to your base of operations or the nearest town. In those situations if the only thing you are doing is resting then the cleric can just quickly calculate the healing effects of her spells and get back to the dungeon. also there is likely going to be a dedicated healer in the town where you are staying who can do the healing for you. For free in a lot of cases. for a fee otherwise. I always give the players in my games the option of bringing a cleric along to do the healing chores if none of the players wants to play the healer, even if one or two are clerics.
I use the specialty clerics rules from 2e. several of the deities in my world do not grant healing spells. Clerics worshiping them have to rely on the same forms of healing as any other class.