If they're going this route, then the user shouldn't be able to tell that an application has been closed behind their back. The application should just be restored when they try to switch back to it.
If the openness of an application should be obsolete, then the user shouldn't be able to tell without explicitly poking through 'ps'
They actually did this, with hiding indicators on the dock by default, but then reverted it in the final GMs. It's definitely the direction they are going in, but it was probably deemed too radical a change for this release. Maybe in 10.8
That's the idea, but when it interrupts the user's workflow, something went wrong in the execution. I care that the program that I am using is open! But Lion pretends to know which apps I am not using and closes them.
A few things happen with an "open" program, like the ability to command-tab through them, appearing in the dock, expecting a window to be in a certain place, showing up in the "Force quit" dialog, etc.
If the user expects to to find an app in the dock, and it's not there, then the user does care if the application is open.
A feature like this doesn't matter as much on an iOS device because of the way applications are launched & managed. Applications are launched and managed differently on the desktop though...
The only loss is that you can't tab between applications without paying attention, but I suspect that many users don't do this anyway.