I think it's worth mentioning, that the achilles heel of DT, is in fact, data (more specifically feature) engineering. If one does not spend significant time cleaning and engineering the features, the results would be much worse than, say a "black box" model, like NN. This is the catch. Ironically, NN can detect such latent features, but very difficult to interpret why.

This varies so wildly from domain to domain. Highly structured data (time series, photos, audio, etc.) typically has a metric boatload of feature extraction methodology. Neural networks often draw on and exploit that structure (i.e. convolutions). You could even get some pretty good results on manually-extracted neural-network-esque features handed off to a random forest. This heuristic begins to fall off with deep learning though, which imo, is a precursor to LLMs and showed that emergent complexity is possible with machine learning.

But non-structured data? Pretty pointless to hand off to a neural network imo.

That has not been my experience though, apart from the need of standard data hygiene that one has to maintain for any ML exercise.

Normalising the numeric features to a common range has been adequate. This too is strictly not necessary for DTs, but pretty much mandatory for linear models. (DTs are very robust to scale differences among features, linear models quite vulnerable to the same.)

One can think of each tree path from root to leaf as a data driven formulation/synthesis of a higher level feature built out of logical conjunctions ('AND' operation).

These auto-synthesized / discovered features are then ORed at the top. DTs are good at capturing multi-feature interactions that single layer linear models can't.

NNs certainly synthesize higher level features, but what does not get highlighted enough is that learning-theory motivated Adaboost algorithm and it's derivatives do that too.

Their modus operandi is "BYOWC, bring your own weak classifier, I will reweigh the data in such a way that your unmodified classifier will discover a higher level feature on its own. Later you can combine these higher features linearly, by voting, or by averaging".

I personally favor differentiable models over trees, but have to give credit where it's due, DTs work great.

What leaves me intellectually unsatisfied about decision trees is that the space of trees cannot be searched in any nice principled way.

Or to describe in terms of feature discovery, in DT, there's no notion of progressing smoothly towards better high level features that track the end goal at every step of this synthesis (in fact greedy hill climbing hurts performance in the case of decision trees). DTs use a combinatorial search over the feature space partitioning, essentially by trial and error.

Neural nets have a smooth way of devising these higher level features informed by the end goal. Roll infinitesimally in the direction of steepest progress -- that's so much more satisfying than trial and error.

As for classification performance where DT have struggled are cases where columns are sparse (low entropy to begin with).

Another weakness of DT is the difficulty of achieving high throughput runtime performance, unless the DT is compiled into machine code. Walking a runtime tree structure with not so predictable branching probabilities that doe'snt run very fast on our standard machines. Compared to DNNs though this is a laughable complaint, throughput of DTs are an order of one or two faster.