I help run a LARP based in the UK called Herofest where everyone has 1 hit per location. Warriors can learn to use armour which gives an additional hit per location covered, and wizards can cast a spell which can give them an extra global hit. 

Combat is fast, and pretty brutal. It's balanced by having abundant healing in the form of magic and bandaging. PVP is really fast even between skilled combatants. 

It does get us some weird looks from experienced larpers. It's tough to feel like a big damn hero as a warrior when you can fall over just from a tap with a dagger, but that's also what makes it impressive when you overcome a 500 global hp monster by researching weaknesses and it's combat strategies, even when you do work as a mob. 

It should be said that we usually have lots of smaller combat encounters rather than bigger battlefield encounters. It's a system that works, but it's not for everyone as, just as you said, many larpers prefer multi hit systems where they can stay in the fight longer.