Schiller truly had to admire Mephisto a little. In a sense, devils were the very embodiment of "shameless people are invincible." As long as they could achieve their goals, they would stop at nothing, and dignity was not even worth mentioning. In a way, they were born with the perfect constitution for the Internet.
And his mind worked quickly too—if he were not clever, he would never have become the King of Hell. While the other Demon Gods were still trying to figure out what the Internet even was, he had already taught himself how to ride trends and hijack other people's traffic.
If he used his true form now, or fashioned himself a new appearance to promote himself and recruit followers, it would probably be very difficult. Not only would he have to build an account from scratch, but unless he pulled off some outrageous stunt, he would not draw much traffic at all.
Devils were greedy. They were not content to gain followers little by little every day. If there was a way to do it all at once, why use such a stupid method?
The movie's screenwriter had already laid out the Character Design for him. He and Barton, the most popular school doctor at the moment, were two sides of the same person. As long as he borrowed Barton's image to display his own charm, would he not explode in popularity in no time?
Although he was using Schiller's appearance, his actual identity in the film was Safir, the most evil dark wizard. And Safir's power came from Mephisto.
If people fell in love with Safir, they would in fact be helping Mephisto expand his fame. After all, many people now believed that the King of Hell was Satan. Even if he could only correct some