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A quick fix for this in OpenStreetMap is to limit ourselves to columns that are populated in a meaningful amount.
For example, by excluding tags that have less of 1% populated rows the amount of columns shrinks dramatically, from over 5000 to a bit less than 100 in the Italian dataset.
Some work remains: lots of columns seems to have similar names and purpose, they could be somehow aggregated but it's something that imho should be done in collaboration with the OpenStreetMap community.