I've been playing jack-of-all-trades in the early game lately and having a blast. Haven't spent a point on any attribute yet, just buying the freebies in several skills. I can one-shot any normal zombie and two-shot the 750xp ones (bloated walker, Hawaiian shirt guy, feral Arlenes, etc.) with a Q1 iron crossbow I bought from the trader (Hidden Strike). I can hunt rabbits and chickens and I have like 200 meat stored up along with a ton of bones and feathers. I get a bit more from the trader, buy for a bit less. Dig a little faster, use a bit less stamina, get a bit more from trees and ores. Can cook the basics - teas and B&E. Can make a forge and iron.
So far it's working out very well, but before horde night 2 or 3 I'm sure I'll start specializing a bit more. I certainly don't feel constrained at all yet.
That said, I do see the argument for separating weapon skills from attributes. Nagana happen, but I'm sympathetic to the argument.