Cheaper, yes. That's my point.
What I read is that early iron weapons weren't necessarily better than bronze (we're not talking about steel here), just infinitely cheaper once the basic problems of iron smelting were solved.
I too had always thought iron weapons were intrinsically better - thinking when an iron sword met a bronze sword, the latter would be cut - but I'm no longer so sure.
Swords don't really cut one another. Mostly they batter the edge dull and possibly chip it a bit. If one sword is very brittle, than a chip can lead to a crack to a full break. Swords don't really cut armor either. Not with just human strength behind them.