Huh? I just tested it now and the App Store reopened on the same page I was on and Safari also opened on this page and it remembered what I had written into the text box.

More generally apps can store whatever info they want when they're going away to be retrieved when coming back transparently.

On the other hand semantics on the Linux desktop are such that the operating system cannot inform an app that it is going away transparently.

An app that is SIGKILL'd cannot save anything (unless it is proactively saving all the time which is terrible for battery life), an app which is SIGSTOP'd must save it's entire memory space and cannot relinquish locks or GPU resources, and an app that is SIGTERM'd can ask the user to save their work etc. (which is not what a transparently closed app should do).