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It's not hard for Apple to maintain this list across device shut down and properly put launch them into a sleep state when you restart the phone.

I'll add some clarity here.

When you send an app to the background it's given time to finish any remaining tasks. At some point iOS will put that app to sleep (suspended). The system expects those remaining tasks to finish quickly so it can spare your battery.

The thing to note is that iOS developers were granted the ability to WORK while in the background in iOS 4 and expanded through later releases. Meaning, we can ask Apple to periodically "wake us up" so we can perform any necessary tasks that may improve your experience the next time you visit the app. This can range from a wide variety of things (while discouraged, devs can make OpenGL draw calls...). While foreground apps always have precedence, an app woken up in the background can go to town on a wide variety of tasks for a short period of time.

So yes, technically, the apps in your switcher are alive and well these days (popular apps have adopted this background behavior by now). Closing these manually will prevent apps from doing any of that background work since a developer can't tell iOS to launch an app from a clean slate.

For those suffering terrible battery life keep that list clean. For those who look for an optimal app experiences leave 'em be.