Logistic regression: What are use cases for logistic regressions where $n \neq 1$, i.e., $n >1$? NOTE: This question relates to Binomial logistic regression. Thus, the $n$ in the title, refers to the parameter of the Binomial distribution.
Most real-world use cases of logistic regression introduced in statistics courses and employed in machine learning models are about binary logistic regression where $n = 1$.
Given that the logistic regression, in general, is based on a Binomial distribution (as can be seen, for example, in the application of logistic regression models in R, where the R library/package, glm, requires the user to set the argument family to binomial, in order to perform logistic regression.
My question is thus: What are use cases of logistic regression where $n \neq 1$, i.e., $n >1$?

Assuming that your $n$ is the number of cases of each type, you end up looking at proportions of each successful rather than $0-1$ and you weight by $n$.
Stealing from https://stackoverflow.com/questions/50078497/weighted-logistic-regression-in-r gives an example of sample data of proportions of successes (prop) plus sample sizes (n) for each value of the independent variable (x)
datf <- data.frame(prop  = c(0.125, 0,  0.667, 1,  0.9),
                   n     = c(8,     1,  3,     3,  10),
                   x     = c(11,    12, 15,    16, 18))

glm(prop ~ x, family=binomial, data=datf, weights=n)

which gives
Call:  glm(formula = prop ~ x, family = binomial, data = datf, weights = n)

Coefficients:
(Intercept)            x  
    -9.3533       0.6714  

Degrees of Freedom: 4 Total (i.e. Null);  3 Residual
Null Deviance:      17.3 
Residual Deviance: 2.043    AIC: 11.43

you get a reasonable model producing a sensible looking chart like 
though you also get a warning about non-integer #successes which you can ignore, and the wrong values for degrees of freedom, deviance and AIC.
