You are correct, but you said 'would we still be in the bronze age', that implies society would've halted at bronze. In any case, the point remains: different alloys serve different purposes. So, assume the easier availability of bronze was a thing, at some point society would reach a point where the ends were no longer met by it. The reasons could be various, but it is hard to imagine human ingenuity would just stop innovating. Consider martial purposes, steel is far better than bronze, assume iron was not relied on that much, the chances of discovering steel are quite likely & and subsequently, so would the urge be to apply it. Hence, my point is that if more availability was around it would plausibly allow the usage of bronze to stick around longer, that is until a superior alloy (like steel) was discovered. No warrior in his right mind is going to choose bronze over steel.