For one, smelting isn't melting/alloying, and I think you're confusing these terms. To smelt iron from iron ore, you still need a carbon source, for instance.
Which presumably would be introduced the same way as it is in magma smelters. Metallurgy isn't really my area so I'm not sure what way that is, but it has to be possible somehow.
Also, this sort of solar array heats things up at a focal point. A big vat of iron would probably have trouble maintaining temperature if you're only heating up a very small portion of it, probably.
This would be a problem with metals that aren't particularly good conductors, but keep constant heat on the focal point and that heat will flow outward to the rest of the metal pretty easily. The only problem I could see happening is heating the focal point up enough to boil it, which might be necessary to heat up a block of certain metals sufficiently via a single point and would make them impractical for use in a focal setup.
And your idea that "platinum can't smelt platinum" is kind of silly. A solar furnace made using silver mirrors could definitely melt silver, for instance, because the array itself doesn't get nearly as hot.
I guess not so much 'can't' as 'shouldn't - it wouldn't be a problem if you were just doing it every once in a while, but if you were smelting ore at a constant rate (as is common for smelters in DF) the ambient heat would get problematic in a hurry.
And since when is HFS that reflective? You're assuming you can just make mirrors out of any substance.
Most metals are relatively easy to polish and extremely reflective when polished, and if you know how to you can buff mud to a mirror shine. (Originating in Japan and called dorodango/泥だんご, polished balls of mud are popular among children and require a lot of time and specific knowledge, but depending on the material can be made almost as reflective as a marble. Polishing dirt and stones to a high shine for no good reason seems like the sort of thing dwarf children would do, but that's neither here nor there.) In any event, I think achieving the temperatures required by HFS forging is ludicrous to begin with, and doing so with mirrors and the sun would probably be impossible even for us.
And the problem with dwarves isn't that they don't have reflective materials. It has to do with the ability and knowledge to build something that huge and that precise with them.
They have a great deal of precision machinery compared to their tech equivalents historically, although I'll grant that given they don't even know how to make lamps it seems dubious that they'd have a grasp of optics as strong as that of gearboxes.
In the end, between how engineering-intensive it is to track the sun even with modern equipment and how slowly temperature tends to move in setups like this even in good conductors, a mirror smelter would probably look kind of like a millstone in reverse: would only require a hauler and the necessary ores, but would operate much more slowly than even a novice furnace operator. Only worth building if you didn't have magma and lack the coal to waste on smelting.