Actually, the problem with remaking Blazing Saddles today is that modern audiences wouldn't understand what it was parodying.
While the "wholesome western" dominated TV and movies in the 1950s, this genre is almost unknown to current movie audiences. Today, all we know are "gritty" westerns, such as HBO's Deadwood or any of Clinton Eastwood's works in the genre.
So, most of the humor would be right over the audiences' heads, even with the subversion of putting a black guy in the typical role that John Wayne or Randolph Scott would fill. Scott was a punchline in the movie, but today, no one remembers who he was. People wouldn't get why this juxtaposition would be subversive.
Other jokes in Saddles wouldn't work because they've been overdone. The campfire scene was hilarious at the time, because movies like to pretend flatulence wasn't a thing. Today, every cheap comedy does at least one fart joke, it's just not that funny anymore.
The movie contained two jokes where rape was a punchline. That would be completely unacceptable today, as it should be. Conversely, we've rethought our history and realized that the "Old West" was built on the genocide of Native Americans. So the scene with Mel Brooks in 'red-face' speaking Yiddish just wouldn't be funny.
Incidentally, I first saw Saddles in 1974 at a drive-in. We don't have drive-in movies anymore, either.