That's entirely contrary to my understanding and implementation of GTD - which is to have daily "scans" of my inboxes to see what tasks have come in since the l

That's entirely contrary to my understanding and implementation of GTD - which is to have daily "scans" of my inboxes to see what tasks have come in since the last scan, bucket them into the appropriate categories/lists/record-keeping systems, and then _close those inboxes_ until the next scan. If anything, GTD keeps me _more_ interruption-free, by strictly ringfencing the times that I am open to processing new task-requests.