I'm in the camp where Java stuff doesn't always run well on my computer, so I'm relegated to using ATMA myself.
Agreed; items that have use across multiple characters at various stages of the game deserve extra copies. War Travs, Gore Riders, LoH, Shakos, Tal's helms, all those lovely cross-class utility things for you & all your mercs. Multiple sets of leveling gear if you start new toons regularly.
There's arguments to be made for extras for lots of reasons, though. Level barbarians a lot? Keep two one-handers of the weapons you like to use. Unless you're rune rich with awesome HotOs and 6x Ist'ed PBs, at least two Wizardspikes or Ali Babas for FCR & MF options. Two copies of claws for any assassin. Two copies of throwing weapons (maybe four if you like Double Throw barbs that much). Do you care about eth uniques that a merc wouldn't use, maybe you have the desire to fill out that ridiculous grail? What about low drop rate elites -- gonna just throw your 3rd Windforce in the garbage (technically, an Act I merc can use the 2nd)?
Variable rolls on items play into it, too. For example: I've ignored a few Strings at this point, then went to look at the one I stashed and see it's got some of the lowest LL & DR rolls possible. Not the end of the world, but it hurts the heart knowing I probably could have had something better in all those things I abandonded. It's not fun when you find something useful, think you have a back up unused item somewhere, toss the item, and go to look later and end up cursing yourself for not holding onto it.
Unlimited stash size, yes. But also multiple stashes. If there's any kind of trophy you want to hold onto, you can always make another stash for random stuff to keep. Maybe you don't need multiple Templar's Mights cluttering your standard stash, but I know I'd be hard pressed to ditch them regardless of how worthless it is.
As an ATMA user, I don't really think about it. My main stash is around 750 sets & uniques, and yeah it loads a little slowly, but not bad enough that I'm worried about purging things. A large amount of my grail is filled out at this point, but if I see something interesting drop I tend to pick it up and put it somewhere. Probably don't need four Wolfhowls. I got 'em anyway. For me, hoarding is a way of life in D2.