I think you answered your own question. Package management (together with distribution policies to make those packages work together) has solved this problem for Linux already, for all software packageable by distributions, which includes pretty much everything needed to make a usable system. An "app store" just makes it easier to get one-off non-redistributable proprietary apps, which Linux historically hasn't cared much about until other OSes started to, at which point a few Linux distributions started wondering whether catering to proprietary app developers would make the system more popular. (Personally, I'd argue that apps follow platform popularity, not the other way around.)