I edited my original message probably right while you were posting this reply.

Main concern with the window it not so much that it takes too much space, but that it "exists" in the task switcher, which can be distracting when Cmd-Tab'ing. Without going full menu bar way, perhaps a way to make it "transparent" to task switcher could help this - in fact maybe a mix between window (for showing current task) and menubar (for actions)