I think you're right that it's related to it being a rectangle and without changing the sensor shape it'd be basically a crop in software.

The cameras are round though so it's only the capture hardware that would need to be fixed. The "megapixel" of the camera constantly increases as well so dropping some of it in a crop may not even matter much in the long run.

I'm assuming the reasons we don't use a square are cost and space. Phones are pretty tightly packed in, every 1mm width you add probably has flow on effects for other things you can't have.

And I am not sure what the limiting factor is but if you add a bunch more light sensors to make it square I'm assuming that comes with additional cost, not just the sensors but now you need to connect up a bunch more to whatever controls it which then might need more processing power or smaller connectors or some other flow on impact.

You could still rotate your phone if you wanted to, it just wouldn't be necessary anymore.