The point is not that EIS is better than OIS - the systems serve different purposes
They serve remarkably similar purposes and can be complimentary. It's actually interesting because your claims sound like what Google said with the Pixel (1) and its completely substandard EIS-based solution. With the pixel 2 they added OIS and complement it with EIS. Everyone eventually gets to OIS + EIS. But while they're trying to be cheap we hear the spiel about why they just don't need OIS.
Because EIS alone is substandard unless you have a fantastically fast sensor or perfect lighting. Which is why EIS samples are always on the brightest possible days. It isn't by accident.