I've always viewed them more as compact and durable e-books... Hence tome-stones...
As others have suggested, I figure they're actually accessed through some form of magicks... It would make sense for the Allagan to work them that way, since it is much more convenient than having to go to a nearby terminal to access the data... You just find that magic on switch, and you probably get some form of holographic display, based on our other encounters with Allagan computing technology... This would perhaps explain why it's difficult for modern day scholars to read them, I imagine we're all fairly magically-inept compared to Allagan standards... It would also mean Garleans can't read them at all, instead they'd have to come up with a technological method to access that data, so they would effectively plug them into Magitek computers to read that data, which would also be a more efficient means of getting that data these days, hence their success with tomestones compared to Eorzeans.
I also refuse to believe bosses drop these things in the quantities we see... More so when you consider the reasoning behind everything rewarding them, is that Dalamud spread them everywhere... That's just a ridiculous amount if, per dungeon, we're getting 100 individual tomestones... Eorzea should be buried in these things and they'd be worth less than dirt... Don't even get me started on why Azys Lla dungeons yield similar/less tomestones, those places should be a gold mine for tomestones... I instead prefer to read "You obtain 100 Allagan tomestones of Esoterics", as "You obtain an Allagan tomestone, it contains 100GB of Esoteric data". Walking out of a dungeon with 3 or 4 is much better for my sanity, though I perhaps shouldn't bother trying to rationalize obviously game-y mechanics like that, I'd go insane trying to figure out how Eorzeas economy hasn't collapsed due to things like the Challenge Log...