There was - at least on paper - also a Saxon Army and (to my knowledge) also an Army of Württemberg existing. A Ministry of War with own orders, rules, ranking lists etc. of the Royal Saxon Army makes no sense if no own Army exists.
The Bavarians were relatively independent because of their single military success in 1866 and the importance of the kingdom for the unification 1871. The others had this famous double-number system like 1. (Royal-Saxon) Leib-Grenadier-Regiment Nr.100. (the "German" number). So the Saxon Army was amalgamed into the "German" Army. In Fall 1914 the German 3. Army was a nearly pure Saxon Army after some transfer of personnel, but the Prussians used the sickness of Armyleader von Hausen to destroy this unwished political and military fact. General von Einem took over and the Saxon troops were send to very different theatres of war.
Already before WWI some more clear-minded officers realised that this organisation with different armys was only creating bureaucracy and disturbances in the chain of command. Saxons complained often they would not get proper information about new Prussian orders. As well the Prussians did not know or ignored the rules of the other armys.