Generally you want to adjust the column depending on their content, not their header... And keep them as tight as possible to display more columns on screen.
The current behavior is also annoying because the "..." added to give the info that the column is not large enough to display the entire header take up some space in itself so reduces even more the header that is displayed
Another solution (other than the tooltips) for this problem would be to offer an option to display the headers on two lines. This would offer more flexibility to adjust the columns as desired with a display of the headers good enough in many cases, because the appearance of the "..." (with the place it takes in itself) would be then probably much less necessary.