If you truly have unordered table data, and column and row swaps give you a meaningful heatmap data, I suspect the new row and column order probably tell you A

If you truly have unordered table data, and column and row swaps give you a meaningful heatmap data, I suspect the new row and column order probably tell you A LOT. Because before, you just had random labels. Now all of a sudden, your random labels admit a meaningful order. That is a huge deal and suggests underlying structure in your labels!