For me "Next Action" refers to the project, not the actor, so I've never inferred a sense of urgency from the term. It's simply the action the has to happen before other actions can follow. You can't have dental work done until you call and schedule an appointment.
I can see how, if you think that "Next Action" refers to the actor, you will feel like you're failing the system when you backslide. But if you think of them as referring to their project, and if they're faithfully written down, then, if anything, they should relieve anxiety, not increase it.
There's a DA newsletter where he talks about how the GTD black belt remains calm despite any number of NAs on his list, knowing that they're captured in a trusted system. Allen has also said several times that the only way you can feel good about what you're not doing is to know what it is you're not doing. Keeping a full account of what needs to be done is the essence of the system, but it's you, not the system, that does the work. A Next Action list only give us a clear sequence of what actions we must choose to carry out for a project to get done. It can't give us timetable for doing them.