Thanks for confirming that setting is currently off. There isn't any need to turn it ON, since this would allow the phone to use both Wi-Fi and mobile connections when one is stronger than the other. While in this same menu though, check to make sure "Keep Wi-Fi on during sleep" is also ON. As for not using any mobile data, Settings > Data Usage would allow you to turn Mobile Data on and off as you like. Calls and texts would work fine like this, although texts with a picture or video would not work unless using a data connection (Wi-Fi or Mobile). Aside from those phone settings though, do you notice this Wi-Fi turning on and off when you are connected to other Wi-Fi signals?
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