Bumping this thread for support. This would be a valuable feature and I’m surprised it isn’t included by default.
The one work around we have here is to move the properties we want to use from the Overview card to the left panel where the conditional logic is possible, but that has a different set of issues so it is not ideal.
I would also settle for conditional views logic. For example, use X contact record view by default, but use Y view if these conditions are true (with a team being assigned to both, and one of them being the default).