Is SMOTE any good at creating new points? Cross Validated has a pretty thorough debunking of class imbalance being an inherent problem for SMOTE to solve.
However, SMOTE is explicitly a method for synthesizing new points.
Is SMOTE any good at synthesizing new points? If so, is there any way to use SMOTE-style point synthesis to improve model performance, even if we respect the natural class ratio by synthesizing points from all classes, not just the minority class?
(I wrote “SMOTE-style point synthesis” because the “M” means “minority”, so it’s hard to argue that we’re doing SMOTE if we synthesize new points from the majority class, even if we use the same approach.)

Here's how I think of it. We have data $(X,Y) \sim P$ and we want to minimize the risk $R[f] = \text E_P[L(f(X), Y)]$ over some function space $\mathscr F$. We do this by minimizing the empirical risk
$$
\hat R_n[f] = \frac 1n \sum_{i=1}^n L(f(x_i), y_i).
$$
Under certain assumptions the argmin of $\hat R_n$ over $\mathcal F$ converges to the argmin of $R$ so this is an appropriate model selection procedure.
If we have $y_i \in \{0,1\}$ for a classification problem then we can rewrite the empirical risk as
$$
\hat R_n[f] = \frac 1n \left(\sum_{y_i = 0} L(f(x_i), y_i) + \sum_{y_i = 1} L(f(x_i), y_i)\right) \\
= \frac{n_0}{n_0 + n_1} \cdot \frac 1{n_0} \sum_{y_i = 0} L(f(x_i), y_i) + \frac{n_1}{n_0 + n_1} \cdot \frac 1{n_1} \sum_{y_i = 1} L(f(x_i), y_i)
$$
so this is a convex combination of the empirical risks on each class.
I'll assume the positive class is the minority class. If we have too few examples with $y_i=1$, then that empirical risk will be a poor estimate. So one natural approach is to try to bolster it with synthetic samples.
This means that our goal is to produce new data points coming from the conditional distribution $X \mid Y = 1$. The better these points are, the better we'll do.
One strategy: estimate $X \mid Y = 1$ via the empirical distribution, i.e. bootstrap. This is what we are doing when we oversample the minority class.
Another option: get new $X$ by sampling along the lines connecting each pair of minority $x_i$. SMOTE does this. If $X \mid Y=1$ is well-approximated by this distribution, which will happen when we'd want to assign $+1$ to the convex hull of the $x_i : y_i = 1$, then SMOTE will probably work well. There's no free lunch and sometimes this will work and other times it won't.
