As @epriestley mentioned in this comment, which I found referenced in a WMF task, someone should open a new task for this feature request. It is currently possible by a workaround to get something similar by saving bookmarks, but it would be nice and consistent with queries if there would be the possibility to save custom filters for workboards.

We are using project workboards for weekly stand-up meetings, in which we discuss what's going on and who is doing what. It is useful to switch to filtered views like "only tasks updated in the last week" or "assigned but untouched for at least a week" to get a better understanding of what's really going on recently.