They do but its not clear to me whether the area where it broke up was actually included in the original NOTAM. The NOTMAR definitely does not according to the graphic shown on the NASASpaceflight stream. They are still live so I can't link a time code but something like -4:56 in this stream as of posting: https://www.youtube.com/watch?v=3nM3vGdanpw

My understanding is that there are areas which are noted as being possible debris zones across the flight path, but that aircraft are not specifically told to avoid those areas unless there an actual event to which to respond.

If my understanding is correct, it seems sensible at least in a hand-wavy way: you have a few places where things are more likely to come down either unplanned or planned (immediately around the launch site and at the planned deorbit area), but then you have a wide swath of the world where, in a relatively localized area, you -might- have something come down with some warning that it will (just because the time it takes to get from altitude to where aircraft are). You close the priority areas, but you don't close the less likely areas pro-actively, but only do so reactively, it seems you'd achieve a balance between aircraft safety and air service disruptions.

Actually, this video is a good indication for exactly what transpired:

https://www.youtube.com/watch?v=w6hIXB62bUE

It's ATC audio captured during the event.