You're correct on all three questions. I think one point is that you get all of that stuff in the same place, and with multiple chests you can organize stuff more. For example, I have a smithing cabinet and an equipment chest. Also, your house is usually more conveniently located than wherever the alchemy lab and enchanting table happen to be in a given city.
The other thing you get is some weapon racks (2 in the house in Whiterun) and armor stands (0 in Whiterun, unfortunately). These let you display weapons and armor, which is a nice little point of customization. I have the Sanguine Rose sitting in mine, and it looks pretty neat.
So no, you don't really get anything new beyond the first container (which is valuable because your stuff won't grow legs while it's in there). So what are the upgrades for? Completionists, mostly. I might not get every house, but I plan to fully upgrade the ones I do, because they look nice. (Also, some of the upgrades to later houses get you, for example, a cabinet full of good potions, IIRC.) The house upgrades are what an MMO player might call a "gold sink", and after all you will end up with quite a bit of it.