But you're treating them as two standalone things - they are not. The War Chant and the Chief go together.
They did until the Chief was removed 10 years ago. And even then, it's not like the Chief was present during basketball starting lineups or football third downs.
Illinois' hands were tied on the Chief decision by the NCAA. They had to remove him or risk losing revenue. This decision was all on their own, had no significant support, never really discussed in public, and poorly released.