It would be too much work to vet every app for good concurrent programming. It's a much better idea to disallow it and add an API with resource controls later. This is the only way to protect users from resource hog apps.
However, you can have an open but idle connection open in the background with only minimal battery drain. That's how pretty much every kind of push notification or IM system works, even on cell phones.
The best way to save battery on an Android phone is to turn off WiFi unless you need it at some point during the day. iPhone will stop attempting to do push notifications and the background Apple apps will disconnect if the only available connection is WiFi.
I'd also like to point out that "I bet the app was poorly written" is exactly the situation Apple is currently avoiding until they are confident they have a reasonable technical solution to it.
