Is there a real benefit to removing applications from the iOS multitasking bar?
In a word, No.

Apple didn't want to hand over the responsibility of application and memory management to the user, and personally I'm glad that they made that decision.

The purpose of the multitasking bar is to allow users to switch between apps and to quit apps in order to open them afresh (in case of crashes or weird behaviour).

iOS doesn't actually allow 3rd party apps to continually run in the background. There are several methods that Apple have provided to developers which allow a sort of pseudo background tasking functionality.

Long and short is, iOS is pretty damn good at managing memory usage and will kill applications in situations where RAM is running extremely low to prevent a total OS crash.

My advice is, let the OS handle it.