1. You can't make mail with bronze, that's sort of a frowny face. Mail is the best all-around armour for most of history. But! You CAN make scale and you can make small plates. You know who used bronze plates for composite armour (i.e. scale shirts and brigandine?) - why, the Spanish. In the 17th c. On the Northern frontiers of Mexico.
Yes, they had steel lances and crossbows and powder arms but they still found bronze brigandine useful against their enemies.
2. Large bronze plates are hella heavy, but did exist in antiquity and in fact quite early, see Dendra panoply probably meant for a chariot-based warrior.
3. Bronze (or even brass) is lovely in the sense that it's very low-demand low-tech metallurgy that can make some high-precision tools and weapons. Anything that needs to be cast JUST SO is best and easiest done in bronze. For example: firearm locks. Complex hilt guards in rapiers and basket swords. Keys and keylocks. Mace and warhammer heads! Whether very ornate, or simple wedges, many were made in bronze all the way into the early modern era.
4. Bronze is of course much better than iron for canon casting. Less likelihood of cannon exploding and killing the crew. Steel is only necessary for when the stresses generated by the powder arms get really intense i.e. not until the 19th c. level of tech.
And now let's consider what happened with societies that went from stone age to muskets in one fell swoop: they never developed many things we consider staples of premodern combat at all, but pikes and ranged weapons are intuitively a decent combination.
That's how Kamehameha beat his adversaries, for example.
So I find your general idea highly plausible/believable as it were. My only real question and it might be a killer is, why is iron so disfavoured and why is steel expensive in your universe? Iron is available pretty much everywhere after all unlike copper and tin.
With firearms and cannon you really couldn't go beyond smoothbores whatever the propellant. For example in the ACW bronze rifled cannon were tried in small numbers (the James Rifle). Erosion of the rifling was very rapid.
Another problem would be what you use for shot. Lead for small arms would be and issue, but you can't fire a bronze shot from a bronze cannon unless you have considerable windage. That would preclude rifling altogether. Bronze on bronze shot with a close tolerance fit would gall the material of the barrel and wreck the accuracy in short order. You could use lead driving bands but lead fouling would be really bad.
Using lead bullets in a bronze firearm, particularly a rifled one would present a problem too. Lead can be used as solder with bronze. Therefore, in a rifled weapon I'd expect heavy leading of the barrel in use. Even a smoothbore might be affected that way.
Weight would be an issue too. Bronze is much heavier than steel or iron
This is very interesting- thanks!
How would stone shot work?
That too would be a problem if you couldn't get very monolithic and hard rock.
One way that might have worked was using paper-mache for the gas seal. This was done with some types of rounds for cannon. Paper patching bullets was also done.
So, if you have a tough paper material or something similar (leather?) you could probably use a lead or bronze round in a bronze gun. It wouldn't work well with rifling but at least it would work.
That too would be a problem if you couldn't get very monolithic and hard rock.
One way that might have worked was using paper-mache for the gas seal. This was done with some types of rounds for cannon. Paper patching bullets was also done.
So, if you have a tough paper material or something similar (leather?) you could probably use a lead or bronze round in a bronze gun. It wouldn't work well with rifling but at least it would work.
Also in, say, a wheellock or flintlock design, would bronze strike a spark against flint in the same way iron would?
Good point. No. Bronze and brass are relatively spark-resistant. Ugh. I suggested firearm locks too, but they'd need steel, wouldn't they. I guess you could fit a piece of ferro-pyrite on the striking surface to meet the flint with a similar effect, but that's another complication that probably holds back scalability.
Ok so bronze based firearms are essentialy limited to matchlock or similar mechanisms
You could use chemical systems, too, if they exist. A gun mechanism could be based on the chemicals used in matches, and caplocks work with bronze (they'd degrade faster, but that's a problem with all firearms everywhere). But matches are probably your best bet unless you want to posit a very advancved chemical engineering culture.
BTW, stone bullets can be made relatively cheaply in a ball mill: you take millstones cut with concentric grooves, place roughly round stones inside them and have them turn until they are worked into spheres. It doesn't work for large-calibre cannonballs, but the technique was used for smaller calibres in 15th/16th c South Germany IOTL, before those went lead or iron. A few of the mills are still in business making high-end marbles and paperweights to sell to Japanese tourists.
http://www.gasthaus-kugelmuehle.de/muehle.php
Also, consider the possibilities of using non-spherical projectiles. Metal arrows can be shot from guns.