I finally 'get' equivalence

no, you don't end up with an image 4 time smaller. The amount of pixels of your sensor vs the resolution per inch of your output method dictate maximum image size, not the size of your sensor.

A 12mp sensor will output the exact same size print product at 300dpi regardless of your sensor size. Same goes for projectors, screens, any output really.

Megapixels/output resolution (dot per inch, pixels per inch...) dictates maximum image size.

The size of your sensor doesn't in any way affect what size your final image will be.