do you really think live tiles take much battery life? well it seems you don't know how they work. deactivating them won't increase any battery life. like on Windows 10 desktop, do you think by stopping them from animating you will be saving anything? no. they work that way for a reason... to give information. end. if you don't want something that rotates you can always have the small size.
There are anyway many alternative apps like you pointed out that probably have the option to disable it, but it's not because of battery life. it's becuase some people just don't want animated tiles.
so I don't understand your point about the battery. there are more options that can impact battery life more, like synching email, how of often app does it. the double tap to wake up feature, the brightness of the screen, how many apps you let run in the background that are not important to have them updated often (like if you only cared about weather app to give you info when you get in the app. not before. or a news app giving you push notifications... these things waste more battery than live tiles) or something like Glance feature, location, NFC, bluetooth, wifi.... many things waste batter more than simple live tiles flipping. so I don't understand why you get a smartphone but you are anyway dumbing it down so much just to save some seconds of battery.
I am not saying it's wrong to do it, but I find it strange your reason it's to save battery life, when flipping live tiles won't increase battery, and if it does, it will be just few seconds, especially if you compare live tiles to the features I just mentioned.
I don't know any weather app with no live tile though, don't really use weather apps, i only know a few like accuweather and things like that. so I can't help you about the list of apps with no live tiles but I wanted to have my little opinion to you.
you can actually change many things on WP to preserve battery... but I am sure if you unpin every app from start screen, you won't notice any real battery increase. what you can do it's see what apps run on background, how you set up your mail, and features that are useless like sending reports to Microsoft.