NO.
Jacketed bullets do in fact wear out barrels faster then pure lead alloy, grease lubricated bullets.
But the barrel life of a .444 Marlin would be measured in the many thousands of rounds, regardless of the type of bullet used.
What wears out a barrel quickly is erosion, from burning huge loads of powder, at very high pressure, and driving the white-hot gas & bullet through a very small hole at extremely high velocity.
The .444 doesn't fit any of those criteria.
What you may have read pertains to very old black-powder rifles. The barrels on those were made of low-grade soft steel, because they were designed only for lead bullets & black powder. And better steel was neither available, or needed.
Jacketed bullets will shorten the life of those barrels.
Your .444 Marlin barrel is made of much better stuff!
rcmodel
