HTM is a good theory and all, but it only explains a very small amount of what the brain does. The brain has a lot of moving parts, and HTM theory intentionally focuses on only a few of them and ignores the rest. This makes it easy to understand and a good starting point for ppl to get interested in neuroscience.
Seeing this I set out to collect the many models of the brain in all of its aspects. Then I tried to fit all of the collected parts into a single monolithic model. The problem with this approach is roughly as follows:
Models can be formulated in both a bio-physically realistic way as well as in a abstract / high-level way. HTM is an abstract model, but there are also biologically realistic formations of the HTM model. For example see: Sequence learning, prediction, and replay in networks of spiking neurons.
If you insist on using abstract models like HTM, then you will find that none of the pieces fit together correctly. Every abstract model is using different abstractions. I thought that with sufficient understanding and effort I could merge the pieces together, but I found that that is neither easy nor always possible. Furthermore, the number of interactions between pieces of the model grows quadratically with respect to the number of pieces.
In comparison, biologically realistic models are easy to combine since they all interact using the common language of physics: voltages and chemical concentrations. My conclusion is that to build more complex models of the brain will require using a significantly higher degree of biological fidelity than the HTM model.