The folks who want "true" multitasking want the phone to act like a PC so that apps are getting CPU time from the moment that the user launches them until the moment that the user closes them, even when the app is not showing on the screen. (Android provides for this model.)
The good side of more multitasking support is that users and developers could continue to think, code, and use apps as they did in the desktop/laptop world.
Here a bad example: I have an app that I wrote for myself. It goes to a popular website and grabs all of the content, storing it offline for my use during airplane travels. This isn't based on an RSS feed, so I can't use that kind of app, and my app grabs the full content, not just a headline and preview. When boarding for my flight begins, I start the app and push the Download button. I must wait for it to finish retrieval of 150-200 articles and comments before I can do anything else. This sucks.
And it sucks because I, as a user, am not annoyed enough to pester me, as a developer, to fix the app. If the me who is the developer were more committed to producing a quality app that was more mobile-power friendly. Fortunately, since it's not yet in the store, I get no complaints except from myself.
The downside of more multitasking support is that one badly coded app can drain your battery. This then creates user demands for task management apps and task killer apps. (I think that simultaneously tapping all four corners of the screen should be interpreted at Ctrl+Alt+Delete!
P.S. I do plan to rewrite my app and release (it with background downloading), but not until the website goes through a redesign, which is expected within a few months.