While there's been plenty of talk over the years about a possible Back to the Future 4, it's actually a blessing that a belated sequel never happened. Director/co-writer Robert Zemeckis and co-producer/co-writer Bob Gale are the gatekeepers of the franchise. They had it written into their contracts for the series that further sequels or a reboot couldn't be made in their lifetimes without their approval. In the intervening 30 years and counting since Back to the Future: Part 3, said approval has not been forthcoming, with the pair making it clear that the story is finished.
In lists of the best movies ever made, Back to the Future is often among the ranks. Its deceptively simple elevator pitch, "what if you could travel back in time to meet your parents when they were your age?" is transformed into a fantastically clever adventure that encapsulates the Amblin spirit of the 1980s. Though its ending tease wasn't originally meant to spawn a sequel, the film’s success resulted in Zemeckis and Gale conceiving a trilogy to tell a bigger story. Back to the Future: Part 2, and Back to the Future: Part 3 were filmed back-to-back, and while they didn’t reach the acclaim of the first movie, were nevertheless successful. Appreciation for the sequels has grown over time, and many have never given up hope on Back to the Future 4.
Notwithstanding fan demand, Zemeckis and Gale are correct that a 4th movie would be a mistake. The Back to the Future trilogy forms a complete story with a beginning, a middle, and an end. The finale of Back to the Future: Part 3 wraps up the adventure perfectly, giving Doc Brown a new life with Clara, and Marty having a world of possibilities ahead of him. As Doc says to Marty in his farewell, "your future is whatever you make it. So make it a good one." It’s an extremely satisfying point to end the series on, and something that any sequel would undermine regardless of quality. There isn't any need to extend their stories with Back to the Future 4, it's far better to leave it on the feeling that they all "lived happily ever after.”
The Back to the Future sequels were filmed only a few years after the original movie, and so retain its tone and appearance. As a trilogy, they feel like they're all part of a singular vision, which Back to the Future 4 would inevitably feel separate from. Too much time has passed. While sci-fi legacy sequels can work (e.g. Blade Runner 2049 or Ghostbusters: Afterlife), they usually come with the prerequisite that they expand the world and add new characters as the main protagonists. The charm of Back to the Future however is embedded in the Marty/Doc relationship, and the Hill Valley setting. Focusing on other characters or expanding the world just wouldn't feel like a Back to the Future sequel, and more of the same would feel superfluous and underwhelming after all these years of fan expectation.
While Zemeckis and Gale have made sure that there will never be a Back to the Future 4 or reboot in their lifetimes, fans still have ways to enjoy the time travel franchise outside of the 3 movies. There is the short-lived 90’s animated show, books, comics, and even West End stage musical of the original film. Perhaps the closest fans can get to a Part 4 is 2010's Back to the Future: The Game (which picked up the story 6 months later), or Christopher Lloyd’s return in the short film, Doc Brown Saves The World. Rick and Morty meanwhile have taken up the banner from Doc Brown and Marty McFly, plotting their own course of modern-day time travel shenanigans.