I don't use the cut page to actually edit, but the one cut page feature I use a lot is source tape mode when viewing rushes and building selects timelines.
You would only need two of the three buttons for mode selection currently in the cut page. So I couldn't see any impediment to adding it to the source viewer window.
I realise it's a bit of a long shot, given that Blackmagic are keen to keep features within the cut page, but hey no harm in asking.