One of Goku's defining characteristics is his insistence on constantly training to become stronger. This obsession inspires him to frequently spare villains their lives, not necessarily showing them empathy but merely guaranteeing that he'll retain a rival who can motivate him to train harder. As a result, Goku is constantly learning new power-ups like Super Saiyan Blue and Ultra Instinct. And it's because of this central component of his character that numerous fans have synchronously come up with Super Saiyan Infinity.
However, this is also why Super Saiyan Infinity is contrary to the "Dragon Ball" franchise's very nature. Since Super Saiyan Infinity is intended to be the strongest possible version of Goku, learning this or an equivalent ability would nullify Goku's core personality trait. While theoretically such a technique might make for a fitting conclusion for "Dragon Ball," at the end of "Dragon Ball Z" he looks forward to a young boy with massive potential named Uub becoming a powerful fighter, making it clear that he's happiest not when he's the strongest in the universe but when he has someone pushing him to grow.
If Goku does ever attain Super Saiyan Infinity though, as Reddit commenter GhoulArtist pointed out in a thread about Lord Aizen's YouTube video, he could always still always aim for the even more powerful Super Saiyan Infinity Plus One.
