I think for this to get support we need to understand it better. Tabs are not limited to active tasks, so how would this be defined for non-active tabs? For example, a planning tab, showing all Projects, or a completed-tasks view, or the Starred view -- should it show 30 tasks but only count the active ones? Can the user specify what to count? It's true that "Active" has special meaning in MLO, but only for tasks themselves, not for views or workspaces.
If really Active is all that is desired, this could be an option per workspace setup. A checkbox, "Count Active Tasks". This way at least we wouldn't be stuck with meaningless numbers on the other workspaces.
However, I'll warn you, I suspect this feature would require significant (though perhaps warranted) changes to the MLO underlying design, because Workspace updates are "pulled" as far as I know - they don't update contents until you activate them and even then when something changes in the background, they only refresh when you switch back to them or change a task while already in the tab. So a count wouldn't be update without a focus change AFAIK.