I stole absolutely every ingredient from the alchemist in Whiterun and her stuff respawned. I stole it again.

That's exactly what I want to do! It's no fun being a thief when there's nothing to steal! Maybe the shopkeepers wised up in my game and are keeping everything under the counter? That or they're practicing their mime routines. Either way, stealing empty air would be fine if I were roleplaying a Spaceball, but not for my current character.
Can I ask how long it took for your shops to respawn? Maybe I haven't waited long enough, though it's been at least a month in game.