This is known as ETTR which stands for Expose To The Right. As you correctly described, this will improve image quality as long as there is no actual clipping. The name comes from the fact the the histogram will be skewed to the right without actually touching the right edge.

There is one more reason why this is good which you did not mention. Sensors measure light linearly, this means that every stop of exposure has an twice as many values to represent nuances within it. So by increasing exposure, you will use more of the higher precision stops. Here is why:

Let's assume a 12-bit sensor. It reads values as 0-4095. Each spot is twice as bright as the previous one but sensors measure light intensity linearly. So the highest stop uses values 2048-4095. The next lower stop uses values 1024-2047, going down until you get to a point where the signal is drowned by noise which is why not all 12-bit sensors can actually capture a dynamic-range of 12 stops.

The further right you expose, the higher the ratio between signal and noise becomes, so noise is less apparent. The same noise is still there but because the signal is stronger, it has a less impact. Also as you can see you have basically 11-bits to represent nuances the brightest stop and 10-bits for that of the stop before that and so on.