Do you use some other block breaker to obtain your ardite and cobalt? I remember bronze not being a high enough mining level to mine them, hence the need for steel/alumite. I do usually make my first few tools out of bronze though, and I hardly ever upgrade from a bronze lumber axe unless I have TinkerTweaks to upgrade individual parts as I deem fit.
Actually, I think you're right.
I was being wrong in the interwebs and for this I apologise.