Convergent evolution doesn't make evolution non-tree-like, that's just a tree with similar-looking branches or leaves at different locations. Pretty standard really. Convergent evolution makes taxonomy less tree-like.

Carcinization is a good example: it makes lots of things crab-like, so from a surface taxonomic point of view a flattop crab, a coconut crab, and marbled crab are all pretty crabby. But they're completely different evolutionary lineages, and only one of them is a "true crab".

Where evolution gets less tree-like is MGEs (https://en.wikipedia.org/wiki/Mobile_genetic_elements) as some of them can move between branches.

> Convergent evolution makes taxonomy less tree-like.

Yes, exactly. "All taxonomies are don't broken" is not at all "incompatible with the theory of evolution," is the point. The taxonomic layer is pasted on top.

Sorry, as stated above I misunderstood "There is no such thing as a tree." to mean that OP though taxonomic trees were fundamentally broken in some way, I misunderstood OP!

That said, if we had perfect knowledge of the speciation process over the years, would our taxonomy not be extremely close to a perfect tree, where every node has 2+ branches, and branches don't converge to being species-compatible for breeding?

I get convergent evolution, but among large (let's say 10g+) organisms, I'm not aware of convergent evolution resulting in compatible species that would not otherwise have been compatible?

I'm super rusty on this topic, but if there is theory that large organism actual DNA-level speciation (resulting in individuals who cannot reproduce together) has eventuated to convergence back to a new species (who can reproduce together), I'd love a source. I definitely could have very rusty knowledge on this but it seems intuitive to me?

I've been saying it for years. Life is not a tree, it's a DAG.