There are also several types of scale armor, and not all of them were instantly abandoned the moent plate came out. You have the more "traditional" fish scale armor, little miniature plates laced over leather harnesses worn over a leather jack, as well as layered, sewn plate armor, which is a type of scale armor, quite popular in Europe amongst those unable to afford a full plate suit. There were also Japanese, CHinese, and Russian armor well into the early modern era were made of variations of scale armor. 

And as for Europe, they did have the brigandine which was a variant of scale - that his steel plates layered over each other forming breastplates resembling the traditional [i]lorica segmentata[/i] of the Roman imperial era - and in the case of the brigandine, it is scale armor only in the sense that it is layered strips of metal: the brigandine grew not out of eastern or ancient lamellar or scale armors, but as an evolution of the coat of plates - that is, a predecessor of plate armor, though its construction (of small squares or slices that were riveted or sewn into a backing vest or similar) does make it somewhat analagous to scale armor.

As for scale's advantages - it is relatively cheap, sturdier than mail, and relatively easy to repair.

Further there's also a metallurigcal point to be made - while it is "easier" in some senses to make a single larger piece of steel of sufficient quality... It also takes a much higher degree of skill and much more time. By this, I mean that when making a breastplate out of just two or four pieces of metal, you get many more chances to screw up while fabricating that singular piece. And if you screw up on any fo those panels, you essentially have to start over with that panel. On the other hand with scale, the time to produce is much quicker, meaning that there's less opportunity to screw up its production - and when you do, you're not screwing up a massive piece of metal, wasting it...but just a single piece that takes much less time to produce.