LotusEater
I brake for blue butterflies
Why wouldn't you store things in there? It's yours and it's convenient. Until I built my houses, I always stored mine in the satchel of my house in Markarth. It is yours and won't dissappear. Where would you store it? In Breezehome it's either in the satchel or in the trunk. As long as Lydia's there, whose gonna steal 'em. Actually, who would steal 'em anyhow - Arcadia?
While I pretty much only use alchemy to create enchanting & smithing enhancers, it does level you up quickly. Plus it's a ready source of cash. Besides, the ingredients are worth next to nothing, so what's the point in selling them. You might as well not even bother picking them up (there are exceptions, of course - void salts worth 125, etc...).
Because if you empty it out, it may respawn with a human heart. I use poison a lot. Of course you have to be away from your house long enough to let it respawn but that's usually not a problem for me. Plus why use a satchel when you got a big fat chest in the same room?