Why beta regression?

Question

According to http://r-statistics.co/Beta-Regression-With-R.html, the topline remark is:

Beta regression is used when you want to model Y that are probabilities themselves

Grammar aside, one may assume that using the default specification, the beta-regression will provide log-odds ratios for response. But why should this method be preferred over quasibinomial regression?

Suppose I generate the Y according to the following probability model:

$$ \text{logit} (p) = -2 + 0.5 x$$

with the design so that $x = [-3.0, -2.9, \ldots, 2.9, 3.0]$ and represent $Y$ according to fractions of 10 independent Bernoulli replications.

`%in%` <- function(x, r) x>r[1]& x<r[2]
set.seed(123)
options(warn=-1) ## stupid default errors for GLM that don't matter
do.one <- function() {
x <- seq(-3, 3, by=0.1)
y <- rbinom(n <- length(x), size = 10, prob = plogis(-2 + 0.5*x))/10
f1 <- glm(y ~ x, family=quasibinomial())
library(betareg)
y2 <- y
y2[y2 == 0] <- 0.0001
y2[y2 == 1] <- 1-0.0001
f2 <- betareg(y2 ~ x, link='logit')
c(
cover1 = 0.5 %in% confint.default(f1, 'x', level = 0.8),
cover2 = 0.5 %in% confint.default(f2, 'x', level = 0.8)
)
}
out <- replicate(1000, do.one())
rowMeans(out)

In this simulated example, even with small replications, the coverage of the quasibinomial model is much closer to the nominal 80% CI limit whereas the beta regression is anticonservative, achieving approximately 70% coverage. Is this not the correct way to construct CIs for a betareg model? Or is this not the appropriate interpretation of covariate values?

> rowMeans(out)
cover1 cover2 
 0.787  0.699