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I don't know for sure but I've heard a hood-liner helps muffle sound; it's a heat barrier helping to preserve the paint on the hood; and, in the event of an engine fire the plastic retaining pins melt and the hood-liner drops onto the engine acting as a fire suppression blanket.
I seem to recall OregonC6 has strong opinions about the hood-liner or "mat" as he refers to it. Hopefully he'll jump-in as well.
The majority of cars I've owned have had hood-liners. I certainly see no benefit removing it. Besides, it makes a wonderful canvas for under hood artwork.
I had one of my cars for 20+ years and the insulation is just starting to come off but after all of these years nothing has happened getting old so it starting to fail.