It wasn't just Mathiu and Shu, Caesar and Elenor did the same and I'm pretty sure Lucretia will be no different. They joined the battles as strategists/advisors (aka support), not as fighters. That's why the Support function was created in S3+, for those characters whose specialty isn't fighting.
However, not all strategists shouldn't fight. Salome from S3 was a decent combatant, for starters.