An ample body of research suggests that leaders should demonstrate inclusivity by treating all team members equally well (i.e., low LMX differentiation), particularly when teams are diverse. Yet, we lack insight into how this inclusivity affects leaders. Does maintaining similar relationship qualities with all team members burden leaders when the team members differ such as in terms of age? Linking theories on resources, age, and leader prototypes, we posit that the relationship between leader inclusivity and emotional exhaustion is positive when teams are more diverse regarding age, particularly when these leaders are younger. Applying Bayesian modeling to a sample of 100 teams (n=1440 employees) and their leaders in a large corporation in Germany with high salience of age diversity, we generally find support for our hypotheses. Diverging from our theoretical underpinnings, we additionally find a beneficial effect particularly for younger leaders of non-diverse teams, prompting further research. Our results imply that inclusivity comes at a cost under certain conditions (i.e., age-diverse teams), highlighting the need for tailored support for leaders responsible for diverse teams.