Wa alaikum as salam,
Brother you raised very valid question and it proves that you are learning things rather having blind faith in anything. Learning is part and parcel of life and we must continue our journey of getting educated until we reach in grave.
There are very certain reasons because of which Imam Ali (as) never took part in any war during the first three calpihs and I can summarize as below-
1. First three caliphs were not legitimate one and they had usurped the rights