I have ridden modern bikes, as well ans "golden oldies", and currently own and drive a modern classic, a 1980 MGB.
There are many advocates to exhaust wrap, and many more against.
Those FOR exhaust wrap claim the benefit of keeping the heat of the exhaust gasses IN the manifold, and therefore claim the engine bay is relatively cooler. In cars... no point in motorcycles...
Example of exhaust wrap in a classic ... In real life, this is a true photo of an exhaust manifold that cracked where the wrapping ended...
Those AGAINST exhaust wrap underline the point that the exhaust manifold is engineered not only to convey the exhaust gasses out, but also to dissipate heat there where it is hottest, the head and the exhaust ports...
...trapping the heat IN, therefore often resulted in warped heads and overheated valve trains...
It is not a mistery that in many "hotter" bikes of the '50s-'70s, the exhaust pipe was attached to the engine head with "finned clamps".
Therefore, exhaust wrap is the "would be tuner's cosmetic snake oil", it makes the bike supposedly meaner, but by no means any faster...
...and... it's a pig to remove, should you ever change your mind...
AND... come to think of it... the Savage already has a twin-layer exhaust pipe, so that what you see on the outside is merely the cosmetic sheath to the real (narrower) exhaust pipe on the inside !