Why doesn’t the SP scale well to numerous fields? The function of spatial pooler is to identify common spatial patterns. The number of spatial patterns grows exponentially as a function of fields. Typically the numerous fields are correlated with real data, and identifying common spatial pattern requires simultaneously learn from all of them. Individual columns in SP has limited connectivity with the input space, it could be hard for a single column to learn from many fields.
From a neuroscience point view, you can ask a similar question, why keep touch, vision, hearing separated at the primary sensory cortices? Why not feeding all sensory information to a single cortical region and let it figure out the common SDR patterns? Within each sensory modality, why having a retinotopic map in V1 or a body map in S1, why not scramble everything together? I think it is also related to the efficiency of learning. It is easier to identify commonly occurring patterns in a single sensory modality at a small scale. The problem gets harder quickly as you concatenate multiple sensory fields together. You can try that with the spatial pooler, I doubt you can detect any meaningful patterns with it though.
Topology means “topographic map” here, which is the ordered projection of a sensory surface, like the retina or the skin, to the cortex. If you look at the primary visual cortex or the primary somatosensory cortex, no cortical column covers the whole encoding space. Instead, each column only covers a small part of the sensory space (e.g., small patch of retina/skin), and neighboring columns covers nearby patches.
The current spatial pooler in NuPIC has the option to use “topology”, meaning that each SP column is connected to a small patch of the input space, nearby columns connect to nearby patches, and inhibition is local. I am not sure how well topology is tested in NuPIC, and I am pretty sure that it cannot handle topology with multiple fields (e.g., vision and touch). I think there could be some interesting projects there.