I think it's the "store" part (and the fact that an "app" is just a thing) that makes it not work. "Store" is about as generic as it gets.
A warehouse, on the other hand, is more specific. In fact I wouldn't even consider a store to be a warehouse... which makes it more trademarkable I think.
Is there a registered trademark for anything that is just... <thing that exists that we didn't invent> Store ?