Generally, at that point, you want to keep the “heat in the fire” so to speak. This helps with secondary combustion and produces a cleaner burn. Once the secondary burn is complete, the gasses are then exposed to the actual interior surface of the stove where the heat transfer takes place which warms the stove, then the room.
My guess is along the same lines as Cozy above. In my Regency, the insulation keeps the heat in, pushes the smoke and any unburned gases toward the front of the stove where they must pass by the secondary air tubes. These supply oxygen to burn the gas and smoke before they have a chance to go up the chimney.
For secondary burn to take place, you need 1100F+ temperatures. The insulation allows the secondary burn to reach and help maintain those temperatures. Without it, particularly with a lower air setting secondary burn wouldn’t be able to reach or maintain those high temps lowering your efficiency and causing creosote.
Usually Kaowool, available online or at a plumbing heating supply house.
Also, it serves in come cases to keep smoke and particulates from taking the short way up through a firebrick or other loose baffle....but, as mentioned above, mostly to keep temps high for better combustion.
It might make the baffle overheat and melt faster - in fact it is likely to! If you are a fabricator, that may not be a big deal.
Wow, kinda like Warren’s pine I’m burning! Thanks for the heads up on the melting steel, Don’t think the benefits outweigh the outcome, I have enough problems using a soldering iron, welder- uh whats that look like?