I do see where you're going with this, though, and I like the concept. However, Luck is one of the domains that does get a game-breaking spell (Miracle), so care must be taken, either to limit whatever else the deity who offers the Luck domain gets (so the build is a 'late bloomer'), or to otherwise limit the power of the Luck domain (essentially, the luck domain trades off powerful Domain Abilities because they get freekin' Miracle).
If a player *knows* that he has unlimited out of combat healing, he won't worry about getting a hit or two, because he knows his healbot can just bring him back up out of combat.
However, if a player knows that his healbot can run out of healing fairly easily, then suddenly he's got a higher level of suspense in combat, and players might not get 'topped off' between combats, making an endurance run feel a lot more like an actual challenge.
It's really the same problem I have with Save States or Reset Buttons like Rope Trick or MMM... if the party knows they can nova and recover completely between combat, they have no reason to NOT nova. However, if they don't have any mechanics by which they have unlimited access to recovery between combats, then they will be more likely to conserve resources, and play it a bit more carefully.
Conversely, it is a greater sense of accomplishment when the players achieve a goal. "Yea, we didn't go with any of your cheat-mode-enabled unlimited out-of-combat healing... we did it the MAN'S way", that kind of thing.