Europeans came up with a better furnace around the 1300s AD that, unlike the earlier ones, allowed the production of reasonably homogenous steel in reasonable qualities; plate armour would not have been viable otherwise. The earlier bloomeries just produced small amounts of steel as a side effect, and getting it out of the chunks of iron was a trick by itself. The edges of weapons and so on could be "built up" of such small bits and pieces, but making armour out of them was somewhat hopeless.
Now, there are of course other ways to temper iron into steel, and those were widely enough known and used. The trouble was that it was very difficult to control the processes closely enough to result in homogenous results in larger pieces (one reason why long swords were so much more expensive than short ones), and indeed even after the developement of tempered steel plate armour laminated animé cuirasses were sometimes used simply because it was by far easier to keep the metallurgy even across a single lame than an entire breastplate...
Mail is neat stuff, and its flexibility (comparable to that of heavy cloth AFAIK) kept it useful for joint protection and such even after as-such more efficient forms of protection (like solid steel plate) became available. Its downsides include a somewhat time-consuming manufacturing process, a certain inherent vulnerability to pointy stuff that can get right into the links, fairly hefty weight, and the blunt fact that by itself a shirt or hauberk will hang from the shoulders and as such burden them with more or less its entire weight. This can be partially mitigated by transferring some of the weight to the hips with a belt, but was nonetheless a bit of an insoluble problem. Stiffer forms of armour could be easier "wrapped" to the relevant body parts, spreading the load more evenly, or simply had better weight/protection ratios (like solid steel plate again - there were good reasons why that became the military norm as soon as economic considerations allowed), but as usual it was ultimately always a question of what facet you wished to emphasize and at what cost.
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