Correct, some of the banking apps I use don't work unless I turn off Developer Mode
It's actually annoying to have to turn on and off every time
It doesn't affect the phone's security in any way, unless you specifically tweak a security-related option in that panel. It doesn't degrade the device encryption or Google Play Services. I don't see how any app could balk while it's enabled. There are no apps I have that even run differently. I use the same banking apps and all the other things as normal, whether or not this mode is enabled for me.
Either way, what Google plans to do is absolutely crazy.