You could certainly take away their ability to use the kit after failing the roll, but I can think of a *lot* of crueler, more exciting things to do with a hard move when one of the PC's is trying to heal someone without really knowing what they're doing:
--the patient survives, but because you didn't know to use the coffee reddener, they went into shock and became paralyzed on one side of their body, oh boy! (Inflict harm)
--the patient survives, but they're not stable by a long shot and you're going through your supplies at a furious rate -- do you let them die or barter all their stuff to that bastard Dremmer for more medical supplies? (Make them pay, or make a hard choice)
--the patient survives and is fine, but is now fiercely addicted to chillstabs and starts stealing from the infirmary, and will do anything to maintain their supply (announce future badness?)
--the patient is still very sick, and only Doctor Balls down by the river can cure them - it's two days ride and they'll need to convalesce for a long time (separate them)
--if it's an NPC patient, he/she rallies, seems to be doing better, then dies during the night after going home. Their family/friends now think you're an asshole. (inflict harm)
--the patient dies right there on the spot and starts haunting the PC who "killed" them. Now you know what to do the next time that player blows a +Weird roll
Any of these options, and many more I haven't mentioned, seems more interesting than just saying "You can't do it". Failed rolls, according to the rules as I understand them, should still move things forward, not result in the player being stuck after a failed attempt. In other words, there's no "whiff factor" in AW.