This sounds like an awkward solution as described. Just enable multi-tasking for all apps but only allow a certain number to run side-by-side. So, I open App X then switch to App Y whilst App X is still running. I then open App Z. When I quit that, I get a prompt allowing me to choose to close X,Y or Z.
A better alternative would be to allow apps to spin off special limited processes that can run in the background. These processes can send messages to the OS to display prompts, and when their parent application is opened, it can communicate with the small BG process to update itself. Then, have a universal drop-down screen similar to Android's notification window that allows these processes to be launched and stopped independent of their parent applications. Processes would either have no UI or a minimal UI in the drop-down. This could then be extended to provide OSX-like services.
This sound kind of complicated, so here are a few use-cases:
1. Writing an email, want to put on some music. Drag down the status bar, select the mini icon for Last.Fm, iPod.app, Spotify...etc. Background process starts and you never left Mail.App. If you then open the App for these applications, they're told the current song information and take over.
2. Browsing the web, want to log on to IM service. Drag down the bar, select the mini icon for the IM application. New IMs will result in a prompt. If minimal UIs are allowed, maybe I can reply through the notification window.
Services could let you do some cool things, like adding location data to an email or quickly SMSing the current playing song.
I am absolutely against the described change to the Dock. If they change it from the way it is now, I'm ditching my iPhone. IMO, in the rush to add features, Apple have entirely screwed up the great UI of the phone. It's now an utter mess with inconsistencies and non-intuitive UI elements darted around everywhere. They're trying to stuff as much information on to the same screen as possible, and it's horrible. They need to separate things clearly and make everything more logical. Nowhere is this more apparent than system settings.
Now people are crying out for home-screen changes. It's a simple grid. Extremely intuitive. It's perfect. As is the dock. You didn't used to need a manual for an iPhone. I've hated most of the changes Apple have made, and if they get rid of the dock, I'll have confirmation that the platform has lost its soul.