Maybe if you had an organization that was big enough to require several blue teams (a military or government?), then you'd need a metric for blue teams. Such a metric would probably compare the sub-KPIs of each sub-organization that each blue team was responsible for, including metrics on customer satisfaction, and warrant investigation if the metrics went under.
The blue teams can't really game that metric without the entire organization falling over, and if that happened, the executives would be to blame, not the blue team.
It's composed of engineers and they analyze existing processes and create new metrics all day long.
They do worry about their own careers/promotions etc but the group is too small for there really to be any opportunities to "game" anything beyond basic politics.
So the metrics are BS, and the company is really being run by subjective intuition, for which th metrics merely provide an impersonal rationalization.
The role of metrics is to grant visibility. Any policies governing outcomes, e.g. pay bonuses for high metrics, those policies are set and iteratively improved by people working off intuition.
Doesn't mean the metrics are bullshit, just means they're a tool.