Well, the tree of life actually has an underlying theory that explains why it would be that way (evolution involves speciation, that is branching only and not convergence) and a transversal cut across the tree represents a particular point in time.

With Ring Species, however, one has to be extra careful. But that is only a difficulty associated with a particular branching point.

Now consider a general classification problem. I give you a population and you have to figure out how many subpopulations there are in it and which subpopulation each individual belongs to. There are parametric models which have problems of their own, but a nonparametric way to do it is to calculate a distance function and then construct a tree out of it. There are bottom-up and top-down algorithms. You described a top-down algorithm. The main problem is that, unlike the case of the tree of life where the tree being represented actually follows evolutionary time in one direction, if you have a group breaking up into four subgroups because of two dichotomies, the order of breaking will make the tree look different and it may obscure the common characteristics between subbranches of different branches.

That is, the tree is the wrong kind of topology in some cases.

We have met the enemy, and he is us — Pogo