This distance that you speak of falls under my use of the word "classify" which now in retrospect is a poor choice of word.
However, as explained by another comment, it does not always become "meaningless". In fact, it becomes variable. For example, if you are interested in secondary structure in your data, you can plot factors 2, 3, 4 or higher against another factor and often the change in pairwise distance at different factors is meaningful.
For example, I've had an example where factor 1 would classify low resolution parameters and factor 2 and further are the only factors of relevance.
When one examined the data, some parameters were in 40 square kilometer boxes and others in more like 0.5 square kilometer boxes. Factor 1 would tell you which parameters are in the 40 square kilometer boxes.
Another interesting example is that one can use this to for example counteract the effects of inflation on sales prices.
However, as explained by another comment, it does not always become "meaningless". In fact, it becomes variable. For example, if you are interested in secondary structure in your data, you can plot factors 2, 3, 4 or higher against another factor and often the change in pairwise distance at different factors is meaningful.