I don't know why you're having so many problems with Mint.
In much the same way as modern Windows, the vast majority of printers will work – to some degree, at least – without any intervention from the user. When the printer is connected, it is detected and set up. Scanners may not be included in this (for AIO printer/scanner), usually because a proprietary firmware blob is required, which cannot be freely distributed.
Brother has offered very good Linux support for a long time. That they also include a script to automatically fetch and install drivers for all of the detected device functions should be something to celebrate – not complain that you have to use a script. If you don't want to use the install script, you can download and install the .deb packages for printer driver, CUPS wrapper and scanner separately and install them yourself, but why would you?