Yes. In truth, that is broadly what I do right now. But I only do so out of broad desperation.
Moreover I was under the firm impression that David Allen firmly and explicitly recommends a single trusted place for ALL your tasks.
But I don't think he demands that all of your tasks be in your active lists that you check several times a day. That's what Someday/Maybe is for.
What happens if I don't have all my tasks in one place, is that I wind up doing much of my life without consulting my task lists at all.
To recap, the core point her is that I read extremely slowly and re-reviewing all my tasks on a frequent regular basis saps my energy and makes me extremely inefficient.
I'm suggesting that you leave the vast majority of your tasks in Someday/Maybe and that you put a tiny subset of them in your lists for the week. That minimizes the daily or hourly reading.