@charlie I hope you don’t mind me continuing our discussion here, but as we were asked to keep the other thread on topic, I thought this would be a better place :)
I think „everything evolved the same amount“ can be easily misunderstood. The point behind it is „everything is up to date“ which means that every species is adapted to their current, modern environment which, as that is true for any given point in time, is roughly equal to „the lineage of every species today has evolved for the same amount of time“.
This also tells us that no modern taxon evolved from another modern taxon. Rather, two modern taxa share a common ancestor (features of which may be more conserved in one than the other)
„Everything evolved the same amount“ does NOT mean, that in every line the same amount of apomorphies have evolved. The rate of evolution in a species is (with limits) proportional to the rate of environmental change within or of the niche it inhabits (as you said, it happens in bursts). Stabler conditions will in general lead to fewer apomorphies & longer times between speciation events.
Regarding hybridisation, I do not think that with the above definition of the species concept (which is the standard definition that I learned, and is also a limiting factor for hyper-splitting species based on genome) it plays much of a role. Lions and tigers or different species of horse can mix under special man-made conditions, but this does not happen naturally. At least not to such an extent that it would affect the population in any significant way.
I do not understand how convergent evolution or mtDNA acting differently would make monophyly less useful of a concept. It would be great if you explained these arguments more.
Overall, however, cladograms only describe relatedness. Not function, form, ecological relationships, or anything else. Of course species affect one another and put evolutionary pressures on each other, but a cladogram does not attempt to show that.
So, I think that a dendritic cladogram is a very accurate representation of relatedness, especially when scaled for time. Speciation and apomorphies are the two central effects of evolution on species. And these can be accurately mapped with a dendritic cladogram and do not require a braided-river-like