How to *integrate* every two frames of an existing video into one in order to compensate for low illumination?
As you note, just adding (integrating) each pair of adjacent frames to make one new frame decreases the frame rate.

But if all you want to do is integrate adjacent frames, consider duplicating the video into a separate timeline, shifted by exactly one frame. Integrating these two streams would give you a new video with the same frame rate, but shorter by one frame overall.

All the rest of the noted issues might surface, but at least the frame rate wouldn't change.