It's a lovely idea - perhaps if you were to extend the scope to other heavy-but-fragile items? After all, how many of us have ordered glassware or ceramics only to have them arrive upside down, with chipped rims and broken handles?
I'm sure a body like the MU would back it if musical equipment were listed as a specialism. There are probably enough horrifying pictures of splintered violins and cellos floating around social media to make such a service seem appealing!