I never really got to use the Ice axe outside of, like, two times, cuz I got the Gretoch pretty early on. So I can't really compare those...
But the range is pretty damn big. One swing can take out 4 zombies at a time if you use it at the right place/with proper timing. There's also the little advantage of the Melee weapons having effin high attack power. Most zombies died inbetween 1-3 hits in my playthrough.
Seeing Brad unload 1/3 of an entire infinite SMG clip for one zombie (and this happens often) just blows my mind
I know. I honestly feel they're doing a bit of a disservice to this game by making it seem like they have no choice(even though they have many,many options to make the combat easier and faster). I also don't think the way Vinny plays is much better, the way he carefully peeks through every corner as if a giant dog will burst through every wall and eat York. Also, Brad has the advantage of not being OCD about killing every single enemy he sees.