Comic book characters adapted to the big screen tend to work best when, at the very least, the spirit of the source material is kept intact. Ironically, when it comes to the Red Hulk, it could be argued that the character makes way more sense in the MCU than it ever did in the comics because of the difference between the Thaddeus Ross of the source material and how he's portrayed in the movies.
For most of his time in the comics before his transformation into the Red Hulk, Thunderbolt Ross wants to destroy the Hulk. Particularly, once it's revealed Banner and the Hulk are the same person, Ross is determined to defeat the monster and keep it away from his daughter Betty. When the Betty of the comics was killed off for a long stretch of time, Ross' quest to protect becomes one for vengeance.
But the Ross of The Incredible Hulk has different goals. He wants to protect his daughter, but more importantly, he wants to harness the Hulk's power. He certainly doesn't care if he destroys Banner in the process, but it isn't his priority. In a deleted scene for The Incredible Hulk, Ross refers to witnessing the Hulk in action as seeing "the back part of God." So for the Ross of the MCU to become a Hulk himself would make far much more sense for his character. For him, it would mean he'd achieved what he'd always wanted.
