I wonder if simply by making the information available on when people are in flow state, a lot of flow state interruptions could be reduced, even without reducing the number of meetings. In particular, encouraging scheduling a meeting at the beginning / end of a flow state period rather than slap bang in the middle would have a big impact. For example, assume you want to work in flow from 10:00-12:30, scheduling a 15 minute meeting at 10:00 or 12:15 is preferable to scheduling one at 11:00, because you might still be able to get into flow for a couple of hours.
I'd like to see a scheduling system which dynamically encourages people to assign other meetings to an already compromised flow period to keep other flow periods free (rather than just blocking things out).
My worry is that without this, just focussing on minimal number of meetings / cost spent in meetings might not be enough. 3 badly scheduled 30 minute meetings might write off a whole day, whereas a single meeting of 1hr30 might have a much smaller impact, but on the raw "time spent in meetings" / "salary cost spent" metric these would seem equivalent.