Reading on, the problem seems to be not really specific to the windmills themselves, but to the fact that Germany is transmitting a lot of power from the North (where the windmills are) to the South (where the industry is). There is also a lot of transfer between Austria and Germany going on (with Austria's hydroelectric pumped-storage power stations essentially serving as batteries), and the Czech's are unhappy that their grid is used for this transmission for free.
You cannot just build more pumped-storage hydroelectric power plants, you need mountains or at least hills, that fit certain parameters and in the places you can build them you will already find them.
Northern Germany probably doesn't have a single such plant but Northern Germany also doesn't have a single mountain, hill or anything higher than a tree as far as the eye can see.
You will find those plants in Southern Germany and Austria but then again they do actually have places to put them.
Besides stopping the windmills or installing plants is not the problem. The problem is that the German grid can't deal with the energy produced in Germany and uses neighboring grids that are not designed to handle that much load.