When looking at the VGchartz numbers of Sonic the Hedgehog 3 on the Sega Genesis it's strange seeing how the previous game (Sonic 2) sold roughly three times it's units. Not that it's unprecedented for games to sell less than their predecessors but even bad sequels can manage to sell more than a third of the last game. Sonic 3 may not be as good as Sonic 2 but as far as sequels go you could do a lot worse.
There's no doubt it has to do with Sonic 2 being a pack-in game for the Genesis during 1993. So why were Sonic 1 & 2 bundled but not Sonic 3? It could be that they didn't think it could compete with Super Nintendo's Donkey Kong Country bundle. It might also have to do with them transitioning to 32-bit consoles around that time, potentially ending Genesis' life cycle.
Some guy working at The Great Escape told me the reason Sonic the Hedgehog 3 was such a rare cartridge over there, was because Sega did a low production run of it. Because with Sonic 2 they over projected it's sales, leading them to manufacture more copies than they could sell off in a reasonable amount of time, thus leaving them holding a bunch of inventory and they didn't want to be burned like again.
Though, since it's mostly anecdotal, it doesn’t qualify as a reliable explanation. However it points out the difficulties involved in manufacturing cartridges, which took longer and were more expensive to make than discs. – In fact I think there's a good chance that other game companies had issues with this. – Regardless, it still leads me to question how well Sonic 2 was selling before they bundled it.