It very clearly exists as a phenomenon. People who deny it are just trying to act like obtuse football elitists. Many non-British players have struggled to adapt to the PL, went abroad and had successful careers.
Some can't cope with the language barrier, others don't settle into the culture or location, weather is always a problem whether people would like to admit it or not, especially to players that have grown up in countries with very warm climates. The style of football is also clearly different in the league, even managers like Klopp and Guardiola have admitted as much.
The fans may not be as fanatical as some ultras around Europe, but that's also due to how well UK laws have been implemented after the very difficult periods during the previous decade. Still, the history and legacy of the game can be ver tough to handle, expectations from supporters and media is always high.
I'm not saying that some of those factors don't exist elsewhere, but it's all combined in a very specific manner in England - there is absolutely no wonder that the PL is the most famous and watched division in the world. Stuff like that don't happen by mere coincidence and it's also why most of the best managers want to work in it, especially in recent times. I can bet that next in line to try their chances would be the likes of Allegri, Simeone, Tuchel, maybe even Luis Enrique.