What you are describing is known as bootstrapping (if sampling with replacement) jackknifing (if sampling without replacement), or (in the case you want to run a significance test, and not simply create a distribution or stats like confidence intervals) a permutation test. I think you already know that; I'm just mentioning in case others want to look these up by name. Also while they can be called 'distribution free' it only means you are not assuming a prefab distribution. If you want to perform a significance test you'll be creating (explicitly or implicitly) a distribution of your calculated statistic (known as the empirical distribution). If you want to be very explicit about this, you can plot a PDF or CDF of your sampled stats just like you could with a gaussian, exponential, poisson, etc., distribution.

We teach these methods to our students in intro stats at UC San Diego. Have been for as long as I've been here (5 years). Last year a data science program was also created here at UCSD. I've TA'd a flagship course in that program too. It's almost exactly the same content; the major difference is imo are the faculty personalities. The stats profs are smug, while the data science profs are energetically self-important. They teach the same shit. Self motivated students with a STEMy personality tend to learn more in the stats courses because the profs drive on hard core theory; on average though, students do better in the data science course because the profs are so bombastic the kids walk out of each class thinking they are basically ready to join the fellas over at Waymo on some machine learning projects - maybe even show 'em a thing or two, cutting edge tricks learned back at the ol' uni.