This reinforces a point I've seen play out in practice. Tracking only the zero-float path gives you a view of where the project is today, not where it is heading.
What I do is run a multiple float path analysis on the schedule and look at the most critical paths, usually the top 10 from P6, rather than just the single critical path. That flags both critical and near-critical activities, and it gives us something concrete to prepare mitigation actions against before float runs out.
I also make it explicit to the project managers which path is driving the completion date now, and which path would take over if delays hit the near-critical chain. It turns a float number into a decision they can act on.
On my last project, the critical path kept switching between two parallel work activities. If we had only been watching whichever one was critical at the time, we would have been reacting after the shift rather than ahead of it.
That is why I agree with Zaka that the path to watch is rarely the one making headlines this month.