I'll have to say I'm not a fan of nerfing the warriors at all. True, they are a very good and cheap defensive unit to toss in your cities, but that's just their speciality. What will nerfing warriors do to the Luchuirp? It's very costly for that civ to make its ways towards producing Golems, not to mention the high cost of Wood Golems in hammers.
I can see where it's kind of a small increase in strength compared to costs of "Warrior to Axemen/Swordsmen", but in general I don't see the in-game problems with such. At the same time, we are talking about ancient military technology "slowly" evolving, where as time progresses, technology increases faster, and military prowess grows faster as well.
There is one thing you are forgetting about the gentleman that is spamming out Warriors early game to defend his cities while you might have access to axemen, in that he is playing "defense". Having to hide in his little fragile cities with warriors, too scared to bring them outside of the cities walls for fear that a higher strength Axeman will cut him down.
Meanwhile the player with the axemen can just station some units on a hill near the city, and go about business expanding his own empire.
Also spamming warriors on the defense has a major drawback of not being able to have an "active defense". So you have a decent stack of warriors defending a city, oh but your enemy is bringing a much smaller group of axemen and a few catapults up to attack. They place their units on a hill near your city, or a forest, or even worse a hill-forest. Suddenly your big stack of "arguably" super-uber warriors are completely useless as the enemy uses a couple of 80% retreat catapults to wear them down, turn after turn, while higher strength axemen make quick work of your weakened warriors. Maybe if you had Axemen in your city, you could go on the offense and make your way towards killing those catapults before they can change the odds against you.
Archery is one of those skills that isn't always necessary, and can be quite costly to pursue. On the other hand, you aren't just simply getting archers out of the research. It leads to the very powerful early game unit of Horse Archers. Not to mention Archery itself allows you to build lumbermills which can be quite beneficial early game depending on your land.
I don't know, I just don't see Warriors vs. Axemen severely affecting my games that much. If we are talking about trying to attack cities, it's when archers and longbowmen start popping up in cities that I groan knowing the losses I will incur when trying to attack the city.
Let's not forget that weakening Warriors will make fending off Lizardmen attacks pretty difficult as well, and they spawn crazy early sometimes!
Removing the useage of Bronze weapons I am definitely not a fan of, this completely removes the bonus of having bronze early (which gives nice flavor to the games).
One thing I will agree wholeheartedly with is that Hunting is just WAY too expensive of a tech. I very very rarely find myself learning hunting, even mid-late game. And it's a total shame too, because there are so many interesting things you can do with the animals before the AI wipes them off the map. Lately in games, even if I speed towards Hunting fairly early and endure the ridiculous amount of turns required to learn the tech, I still find myself lacking in suitable Subdue Animal kills. Usually once I can squeeze out a few Hunters, there is barely enough animals left for me to kill to even get the XP required to get to the Subdue Animal promotion.
I'd like to see a reduction in the beakers for Hunting, and perhaps some sort of tradeoff for the Hunting Lodge. The building itself can give some nice benefits depending on your resources (+1 health, +1 happy). Perhaps the amount of hammers on a lodge could be reduced, and in turn, is it possible to restrict the +health/happy until a specific later tech is learned? Perhaps restrict the Lodges city benefits until the next Hunting/Animal/Nature tech is learned?