Being the basis for engaging multi-starred Titans and stronger opponents in War both which provide more and better rewards especially being victorious. It would be beneficial to newly formed alliances and new leaders to have this information.
Alliance score is a total of the trophy score, titan score and war score. And alliance score has nothing to do with your war opponents and I don’t think it has anything to do with titan star levels after what ever the requirements for getting a 1* titan may be. But I may be wrong on the titan part