For an in-universe answer, the first draft of Furious 7 (then titled Fast & Furious 7) actually featured Sean coming to Los Angeles to work with the crew, much to Roman's dismay as he didn't believe in drifting or that a kid was friends with Han. However, his entrance did not involve going to Tokyo, and rather ending with the hospital scene with Dom announcing he's going to Tokyo, it cross-dissolves to the funeral, where Sean is present and crying.
Roman asks who he is, and claims he didn't know Han, but Tej backs up Sean, claiming how they "rolled together" in Tokyo. And Sean tells them that Han was his friend and wanted revenge.
Roman continues this rivalry, even trying to make sure Sean wasn't with them when they drove their cars out of the plane. But by the end of the film, he accepts him as part of the family.
(Fun-fact, Hector was also going to be the main character, possibly these two to replace Han and Gisele).
Well personally I would've enjoyed this, this wouldn't have worked out as Furious 7 and Tokyo Drift link up, meaning that Sean would've still been 17 and thus not allowed back in the US.
Why they ended up removing this plotline I'm not sure, but potentially it's due to the same reason why Black wasn't in The Fate of The Furious, because of scheduling conflicts with NCIS: New Orleans. It should also be noted that Black will not be returning to Fast 9 either, despite the news that he signed the contract for three films.
Potentially Black will be in Ten and we could get a spin-off about what he did after Tokyo Drift, but these are just faint-hearted hopes.
This video here helps explain what I've mentioned here, as the user bought a copy of the original script and it's confirmed that what is in it is true.