Yes it’s very good and only a part of the story. He died early but other research both predates and follows his work, and work has been done to integrate many different threads to gather together a more complete and accurate picture.
Maslow stands out because he did some ground breaking work with a modern underpinning, but there is earlier work that goes deeper as well as higher up the hierarchy, work since Maslow has made progress trying to pull all this together.
One of the things we can see from this diversity is what is in common and as you note, common across cultures, making it a reliable way to look at what it is to be human and indeed the individual self. This doesn’t mean that cultural and other externals do not affect development though.
One of the benefits (and I think Maslow’s timing is why he’s relatively well known) is that understanding this is a way for those with the resources and time (those who make it out of striving) can use these models to understand and foster development in themselves and others. In fact working with others, working together is one of the best ways to do so, and the sixties was one of the times when this knowledge became widely accessible to people who were through striving, enabling relatively large numbers of people to come together to explore and realise their “human potential” in the sixties, beginning on the West Coast of the USA. That is just one instance though.
This work has been going on much longer, but the sixties was a time when it was able to grow and become accessible outside restrictive frameworks, and offer a more meaningful alternative to those frameworks that were looking out of place to a modern, educated population. A creative impulse that is part of, and part behind a change that was integrating the modern and the ancient “truths”, as well as building on them.
It’s interesting to find that many of the modern techniques which began to be developed to help personal development at that time can be found in other cultures and traditions going back centuries. Historic techniques, rituals etc were also borrowed, tested and incorporated into personal development, therapies etc.
For some, the introduction of the idea we can foster or own development is a revelation and can cause big changes - leaps in development of the individual and those around them. But at various stages there is a tendency to stop, to pause, sometimes get stuck. One of the ways to examine this is with identifications and polarities. For example this manifests in tradition.
Interestingly there’s a dialectic between tradition and innovation. You might be stuck in (identified with) either so I’m not sure if these are in fact stages in relation to each other (which might explain my misunderstanding when presented as layers in the hierarchy - again it depends how Chris defines his categories).
Once you’ve explored both polarities of a dialectic they can be used by switching from one to the other according to what’s needed in a given circumstance, enabling you to move around in the world more effectively (like having two feet rather than one) but then there’s a sticking point (a plateau) where something new needs to emerge that is both, and also completely new (a synthesis). That leads to a new quality, another part of a polarity (a new plateau) to be explored and so on.
That’s just one model of something much more complex and wonderful. 
