When is it favorable to not visualize univariate data using empirical CDFs? A straightforward question: when is it "favorable" to interpret visualizations using, say, boxplots, histograms/density estimates, versus empirical cumulative density functions (ECDFs)?
I've always relied on histograms and density estimates for getting a sense of data distributions, and boxplots for comparing distributions. However, the above methods summarize and discard information. ECDFs do not. Several advantages of ECDFs include: non-parametric, easy to identify quantile values and outliers, can identify stochastic orders at a glance, is independent of tuning parameters, can exist where densities shouldn't (e.g. mixed variables of discrete and continuous), and so on.
So, again, when should I prefer other techniques over ECDFs and why aren't ECDFs more common/standard in data visualization? Maybe my latter claim is false, but from experience, ECDFs aren't all that common in data visualization.
Relevant discussions and article:

*

*If the sample size is > 100, which graphical summarization is the best?


*What does a Barplot, a Boxplot and eCDF represent?


*Are CDFs more fundamental than PDFs?


*Why we love the CDF

Consider the following sample of a thousand observations from a gamma distribution with mean $\mu = 15$ and median $\eta \approx 13.37,$ with numerical summaries below.
set.seed(2022)
x = rgamma(1000, 3, 0.2)
summary(x)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.236   8.673  13.495  15.013  19.939  53.914

Important advantages of the ECDF are that it does not depend on arbitrary choices and does not lose information. Often an ECDF of a sample of moderate or large size seems to give a closer approximation to the population CDF, than a histogram approximates the population density. In the figure
below, the choice to use ten bins for the histogram is arbitrary. Someone familiar with ECDFs will
have no trouble finding the approximate median and quartiles.

R code for figure above:
set.seed(2022)
x = rgamma(1000, 3, 0.2)
par(mfrow=c(1,2))
 hist(x, prob=T, col="skyblue2", ylim=c(0,.06))
  curve(dgamma(x,3,.2), add=T, lwd=3, 
        lty="dotted", col="brown")
 plot(ecdf(x), col="blue")
  curve(pgamma(x,3,.2), add=T, lwd=3, 
        lty="dotted", col="brown")
par(mfrow=c(1,1))

However, histograms are familiar to many non-statisticians. They clearly show the approximate
mode of the sample and show whether the sample is skewed. Also, the balance point of a histogram
gives a good intuitive idea of the mean of a sample.
Boxplots show skewness clearly and explicitly show
the median and quartiles of the sample. They also
call attention to outliers. But they do not give
an intuitive idea of the location of the mean.
Ordinarily, boxplots should not be used for samples
with fewer than about ten observations.

boxplot(x, horizontal=T, col="skyblue2")

Dotplots and stripcharts work well for small samples but can get very cluttered for large sample, such as the one illustrated above. By contrast, histograms and ECDFs can be almost useless for very small datasets.

par(mfrow=c(2,1))
 stripchart(x, pch="|")
 stripchart(x, pch=20, meth="jitter")
par(mfrow=c(1,1))

This is hardly a complete discussion of graphical descriptions of data.
However, just from these few plots,
I think it is fair to conclude that each of these
graphical summaries of a dataset has advantages and disadvantages. Which one(s) to use depends on
the sample size and the properties of a sample
that need to be emphasized in a given situation---and for what audience.
