"A new battery will appear to help, but it is only putting a bandaid on the issue. The new batteries are new and will of course be able to perform better than the battery it replaced. The key takeaway from most folks posting here on the forum is that Apple themselves confirmed that their batteries are in fact healthy, so can only deduce that this continues to be a battery bug with iOS 10 (along with other bugs!)" Dear feinepotte, I sense your frustration, and no maliciousness, so will do my best to answer you diplomatically. In fighter tactics it is called the OODA loop, invented by Boyd. In science, sports, technology so on, we call it ODA, Observe, Document, Analyze. All you have to do is save emails or resolution stories and you know what happened. This is why you can count on one hand, few fingers, those whom had a healthy battery replacement fix. Two were recalls. The vast majority of others had old or expired batteries. Some had outright full phone replacement. It matters; if you look yesterday, one at Genius Bar , whom argued for days his is IS FINE, only to return reporting Genius Bar found his battery not even pinging/registering in diagnostics, or paikinator, with 20% health iPhone 5. They are ten percent so it all matters at pointing out that it is not how you worded it... if you go reread the entire forum, many resolution stories are missing. Some had Apple Support resolve it, but came back here with insults, so were deleted. Or two with DIY risky 3d party options, not approved by forum guidelines. And so many users here still awaiting for /going for diagnostics right now, so NO, what you wrote about most users having Fine batteries, is, factually, not quite so.. Especially for iPhones 5,5S or 6 with 700+ cycles. If anything, stories with Fine/Recall, or genya's low cycle/Fine battery are quite rare. And, yes, as people's success stories come about and corroborate technical science, across countries advisors say the same thing, or in time, having been told the same years ago, put yourself in my shoes and understand why I answer, at times, very assertively on specific points. Like, for example, uncontrollable, unsolvable drain and shutdowns are not normal and, in engineering, always, always, always taken as a circuit issue.
Voicemail bug: GOOD NEWS- you are the FIRST one to report it an NO, it is not an iOS 10 specific issue. It is a random iOS issue. Nor a battery issue. Like the earlier brightness story, they are just bugs, read seen or had them for 7 years. Apple Support, Forums or even Genius Bar should resolve it for you. Reset or advanced Genius Bar firmware resets usually resolve them.
So, I recommend you take it step by step; resolve the software bug first; then isolate the shutdown issue.