What little lore I've been able to find in game and from TIL suggests it was used to bury
the Nord dead in general and nothing says it was used only by the Nords on Solstheim.

From that you would think that it should be found in Skyrim and not just Solstheim. Maybe
it's missing entirely from the mainland because it has been depleted? Even on Solstheim
it's a rarity. Not every dead Nord was buried in it and I believe their were only 27 pieces
that could be mined in bloodmoon and once it was gone, it was gone forever.

Any comments and speculation welcome.

Well, maybe the conditions necessary to create Stalhrim can only occur in particular places on Solstheim. Certain wind currants, certain minerals in icy waters. It's never really explained how the tombs are encased to begin with.
Natural conditions are the only reason I can come up with.

Lore from Morrowind stats the Nords only used Stahlrim to bury the dead that they couldnt take back to Skyrim.

It was in some NPC dialog.

e:nvm

Well, if it is anything, it is an incredibly natural sarcophagus. It's creation, however, that's the real quandary.
Ooh, maybe it's concentrated Frost Magic.

It's Skaal magic, not standard Nordic stuff.

Apparently it's an Atmoran thing as well though, which does make you consider why there's stalhrim on Solstheim and not in Skyrim. Perhaps Solsthiem was originally a part of Atmora that broke off and moved towards Tamriel? I Dunno.