[Q] Does high-dimensional cross-tabulation make sense?

I'm working on sorting some high-dimensional data into clusters. The data includes continuous, categorical and binary features. After experimenting with 0-1 scaling and K-means (so basically coercing everything to numeric), I had the idea of instead converting everything to be categorical (by discretizing the continuous variables into bins) and then finding the counts for every permutation of variables, then choosing the top k as my most interesting clusters.

However, from what I've read it is only common to cross-tabulate 2 (or occasionally 3) variables. Is there some reason it isn't done on a large number of factors?

(I would of course be happy to hear any other feedback on my plan. TIA!)