Actually it's a bit more complex than that, there's a good reason Genius clear app from app switcher for troubleshooting (although arguably they might be doing it too much), while in normal usage it should actually be better if you left app in app switcher. Note that I didn't say leaving the app "open".
The reason being there's low correlation between the fact that an app shows in app switcher, and the app being in memory or running. Given the limited resources, iOS automatically manages memory, quitting apps that hasn't been used recently when more memory is needed, but app switcher only shows the last couple of app used, regardless of whether the app is in memory or not. If this works correctly (and hopefully it does most of the time), then when you remove app from app switcher, iOS will force the termination and clear the memory even though it's not short on resources. This actually leads to worse battery life and performance because if the app is a frequently used one, it will be kept in memory more often after you left it, and when you switch back or open it again, it doesn't have to start all over again. If you force its memory to be purged it has to do the extra work to start again every time, using more time and energy.
Now it's also possible that one of your app's (or its background process) will go rogue, in which case you have no choice but to forcibly terminate it by removing from app switcher. It's entirely valid as a troubleshooting measure. Although if it's not even running right now that does nothing, or just purge the memory, as a user you can't really tell for certain unless you hook it up to Xcode and examine the processes in instruments.
TL,DR: genius bar clear your app switcher (which may or may not actually "close" the app) as a valid troubleshooting measure, which you can also do when something doesn't feel right, however doing it regularly most likely lead to worse battery life and performance.
on topic: my 5S has worse battery life on beta 4 than beta 3, not sure why... i would say it went back to beta 2 level, barely enough for a full day :s
The battery and performance benefits of leaving something in the switcher are lost on anything you don't open often enough though. So why bother keeping something in it that you only open every 2, 3, 4, 5, 6, 7 days? (Yes I know iOS handles the ram and everything on its own, that's not what I'm disputing.)
Isn't the app switcher basically an app itself within iOS? It has to remember everything you've opened and never force closed. The more you toss and leave in there the more it needs to remember. (Not talking about wether all the apps are running or not, I mean the app switcher.(app?) itself.) I've heard of people with 100, 200, even 300 installed apps. Surely this would have a toll if they were all left in the switcher 100% of the time? (Again I know iOS handles the individual apps themselves in memory.)
I'm not saying my "idea" is how it works. I'm simply just trying to think and come up with ideas as to why some people have a much worse experience with any iOS version compared to most. I keep my switcher fairly clean and only keep Safari, Mail and Messages in there 100% of the time. Everything else gets the boot because I don't use them often enough to have them still in ram by the next time I use it. Thus no risk of anything potentially causing issues. (And no mile long list of cards in the switcher.) I've never had a slow iOS 8.0, 8.1, 8.2, 8.3, 8.4, 9.0 even when I was using a iPhone 5 (now 6 since 8.3 beta.) and battery life is almost always great (right now I'm 8 hours 15mins screen and 26 hours 20mins standby with 15% left. And not using low power mode.)
Again though I'm not saying that I'm right or as someone else liked to call it (I know more than Apple does about their own iOS.) I'm just trying to "brainstorm" and discuss what could cause slow down for some. And this was just an idea I thought about.