I wrote it would give instant hit points to X if the hp is under that X (the example was 10), it not enough to fight against zombies but enough to flee and survive some damage on the way home.
The problem is your idea requiring extra attention and understanding while the player mow down countless enemies. They grabbed my pc or not? Do i have enough hp left to sleepheal? The standard hit point system is a good in a game where a single protagonist fight against countless enemies, because it gives a clear picture at glance.
I totally understand a hunt for a medicine is fun and adventurous. But when you just survived an explosion, bullets, etc and left only with few hp, it would be a prolonged death sentence. More hp or less damage won’t solve this because no matter what, this can be happen. And it is bad.
Already too easy to lure zombies one by one to the player, you idea would make the player unbeatable. Running into multiple zombies and fight is stupid, but everyone saw a zombie movie and know that. 
Also if easy to kill them then i would call them pushovers. But i agree, zombies can be too strong for a beginner, but i don’t think it is a big problem - because there are plenty of workaround -, except the fast zombies and the zombies with ranged attacks, they can slow down the character and then the player is out of options. Anyway, as the player get some equipment they become a pushover anyway, but it is an old problem, there are huge difference between monsters, thanks to the “arms race”. They should change everything to make the monsters dangerous but managable. But it is very difficult, i don’t think it will ever happen.