You may find helpful this thread:
Hard Edges: Processing and Organizing
I think the separation of the Five Stages of Workflow doesn't necessarily mean that you have to batch everything. I absolutely agree with the post about having a separate Collection phase to help stop the constant interruptions, and I also agree with the concern about missing truly urgent things.
I think the intent is to approach each phase with the correct frame of mind, no matter if you do them immediately back-to-back. When you are collecting, you are just supposed to be creatively free-ranging, gathering any and all input or thoughts without judgment. You can then switch to Executive Processing mode, and really think about what you have to do about what you just collected. If you have to do something, and you can't do it in 2 minutes right now, then you can immediately think about the right place to keep that reminder (Organize).
It is unrealistic to expect the world to divide up into neat phases, but I think that with an understanding of the purpose and approach for the phases, you can do them in the moment, still keep them separate, and stay on top of your game.