There's the blast furnace for ores, the smoker for food, so why not another one for stones? The melter is a furnace variant that smelts the stone (and glass) recipes faster (e.g. cobblestone -> stone -> smooth_stone)
Only the vanilla stone smelting recipes can be melted. However, other mods can just create a recipe json for their stone smelting recipe:
{
"type": "melting:melting",
"...": "..."
}