I really hate to repeat myself, but the reason for my question is that this doesn't work. My "Ask to Join Networks" is set to OFF. My home wifi connects automatically because I set auto-join to ON for that particular network. Still, some networks, e.g. my work, don't have the option to auto-join. This has nothing to do with my phone, it can only be a network setting.
Again, as stated in the OP, I'm trying to find out if there is a tweak to enable auto-join on all networks.
Right, on the off chance that were all at crossed wires here, let me try something else.
At the very top of the settings screen for an individual network, there should be a button that says "Forget This Network." If this does not appear then the wifi hasn't remembered the password for that network, even if you are currently connected to it, meaning you will need to tap in the password again when you leave and return to the wifi area. I had this issue myself on my iPhone 5 and the way I resolved it was to make sure the network was forgotten, then
manually type in the name of the network into the 'Other' box exactly as it appears on the screen, including caps etc. Choose the correct encryption, tap in the passcode and try that. You might find that the "Forget this network" button now appears and the phone has remembered the network for future use. If this is your issue, this has been reported before, including by me.
By the way, Cleverpin is a great tweak that means that whilst you are in range of a trusted wifi network (as input by you into the app), your lockscreen passcode will be disabled allowing you to just open your phone without having to type in your code. It doesn't do what you want above.