20% more battery life with 2/3 the battery? Those seem like awfully optimistic numbers, do you have the calcs?It wouldn't need it if in the revision Nvidia made the Tegra XI on an 16nm node. Nintendo would be free to reduce the battery size by a third and still have at minimum 20% more battery life than the current Switch.
As for the mockup the screen will never be that big. It costs money to go bezelless. You can save money by making the screen smaller. They will definitely shrink the screen and potentially even have more bezel. At that point I hope it's 540p if possible. Otherwise they will still make it 720p in order to maintain the aspect ratio.
Your confusion stems from the assumption Nintendo would agree with you that there wouldn't be confusion over making an integrated controller device.
I assure you that when Nintendo conceived of the 2DS they definitely of the same mindset that they have to make a distinct brand name for such a revision and would never call it a Switch mini. Any Switch at all times needs to be able to have a portable and TV out mode.