I don't have to imagine this, though, I've done it on iOS. It works fine, because you're rarely working with 1000 items at once. With pagination, you cache the old results, and only calculate the new 50 or so rows at a time.
For something completely client side it is possible either to specify a fixed height or change the smoothScrollbar attribute of the listview (it is more expensive though and not used very much).
Nobody complains, I guess everyone is just used to the way it is. :D