This makes no sense. The reverse problem is much more serious. An early rush with bronze warriors: You quickly research mining - if you discover copper just build warriors in all cities and tech towards bronze working. When you get to bronze working you can immediately have, e.g. 8+ str4 warriors to launch at the nearest enemy who is screwed if he or she does not have copper (which they probably won't have).
First, the parts I highlighted in bold from your post contradict themselves. If the enemy probably won't have copper, the same holds true for the player in question, unless the player is somehow immune to the laws of probability. Therefore since it is probable that neither the instigating civ or the victim civ have copper in their first city, the reverse problem can't be much more serious. Working under the assumption that you will get copper in your first city is great, but 9 times out of 10, it won't work, and really makes this entire thread a moot point.
Second, more often than not in recent games, I noticed the AI getting archers. Lots of them. Since Crafting->Minning->Archery is now viable (and in fact archery is cheaper than bronze working) the AI can defend themselves very well if attacked by bronze warriors and not possessing copper themselves. Since bronze warriors require more research and there is a delay between getting bronze weapons and getting the units to the enemy cities, the enemy player has more than enough time to field archers. Taking an enemy city with bronze warriors vs. fortified archers+promotions+cultural deffense/hill/palisade is not a strategy that is prone to success.
Rushing axe-men on the other hand is a very different business. You either have to have _a lot of cash_ (which will slow your research and your rush) to upgrade your warriors _after_ building a training yard or you would have wait with building axemen until after the yard is constructed. All things equal, an opponent will have the same time to research archery and make some archers which can hold their own against axemen.
Well, to your point about archers, they will be doubly effective against bronze warriors because of their higher strength combined with their innate bonuses, city defenses, promotions, and their first strike. Without cats, you'll be lucky to kill 1 defending archer without reloading. So your overall argument in that sense is mildly self defeating.
Also, about the use of the term "rush". Bronze working will take about 60-80 turns to research assuming you ignore education and other techs necessary for economic growth (assuming you don't start with gold or gems in your bfc) which may gimp your civ in the long run. By that time, there are any number of available counter to a rush, some of which have already been discussed. Note: the above assumes normal starts, not advanced which gimps the game in favor of the player and certain broken strategies.
It should be pretty obvious, but I voted for the "No, don't change option", as by the time you can get the bronze warriors, they're only viable in either a defensive role or as a support role for stronger units (assuming a competent opponent). However, If you really feel that any of the suggestions would make the game better, it would be a relatively simple matter to bring about the change via xml iirc (particularly war kirby's last suggestion about bumping warrior strength down). Test the change for yourself, and if you like it, keep it.