Some of my all-time favorite issues of the Avengers were during the Micheline era, when Beast was an Avenger. I was a fan of the X-Men going back to the Neal Adams issues, but I liked Beast better when he was blue, furry and an Avenger.
Even so, I don't think that Beast belongs with the Avengers.
Beast is a mutant. His early experiences as a hero were as one of Xavier's students and as an X-Men. However unrealistic it may be for people to discriminate against mutants and not the other metahumans, that is how things have worked on Earth in the Marvel Universe. For better or worse, this is a major issue for most mutants, although they have chosen different ways to cope. As an intelligent and highly-educated scientist in various bio-sciences, Beast has provided valuable assistance to his fellow mutants. They need him, and he knows it.
As an Avenger, Beast was often portrayed as feeling useless or awkward. His scientific skills weren't necessary, as the Avengers already had geniuses like Tony Stark, Hank Pym, and T'Challa around. He was nowhere near as powerful as the heavy hitters like Thor or Vision, and frankly less skilled at combat than people like Captain America or Hawkeye. It was nothing to be ashamed of, but Beast just didn't have anything that the Avengers needed the way the X-Men did.
Allowing for variations from writer to writer, Beast seemed very out-of-character while in the Avengers. So much so that I don't blame Michelinie because it was deliberate. Being an Avenger for Hank was like being on vacation. He could fight costumed villains with the help of Earth's mightiest heroes without worrying about murderous bigots who wanted to kill all the mutants. These heroes knew him more by reputation than anything else, so Hank was free to re-invent himself with them. That's why Beast as an Avenger was so carefree and happy, where he is usually depicted as being calm and cerebral when he is with the other mutants. But every vacation must eventually come to an end, and Hank couldn't ignore the needs of his fellow mutants forever.