Oh I see what you're saying. But I will point out that they successfully do IRV with paper ballots which includes many rounds of moving said ballots around. You wouldn't have nice piles with Approval, but it wouldn't be too hard. You're always going to have to add a little complexity to get benefits. The thing though is that Approval is the least amount of complexity we can add, and it gives surprisingly a lot of benefits. Maybe sorting would be a little more straight forward with Score or STAR voting since you can bin them on the highest score. These do have more benefits too and are actually preferred over Approval.