Nah, I think you just fundamentally misconstrue the story structure built around these characters.
I'll say it once more: Vegeta's current rivalry with Goku is no more of a "goal" than Goku's constant self-improvement, Piccolo's constant meditating, Gohan's constant studying, etcetera. It's Vegeta's hobby written to specifically underline Vegeta's perfectionism as a fighter, often narratively used to exposit him in Super's various arcs while having either absent or ancillary (at best) bearing on his core growth in those arcs. It is subsidiary in every possible sense of the word. It, too, is in a psychologically healthier place now that Vegeta isn't pursuing it with the same self-destructive tendencies as in the original manga, which also demonstrates how much he's changed.
There isn't a single story arc in Super that puts more emphasis on this rivalry than on Vegeta's development when faced with other characters or personal demons, be it Cabba, Zamasu, the Namekians, Granolah, and so on. Super Hero goes even further and actively mocks it by largely off-screening his match with Goku while the tone and dialogue lampshades his "victory" at the end. That's Toriyama telling you how little it matters.
What a bizarre thing to get hung up on just because T&T are more invested in a character that by far has more dimensionality, nuance, depth, and focus even in the original serialization than... Tien, lol.
Yes, and the Super Hero story worked because it uniquely benefited those characters and their development, which, much like Vegeta, also had quite a bit of relevance/involvement from their introduction in Toriyama's manga all the way up until the end of the Boo arc. Quite frankly, it's so much easier to imagine a dedicated story for them that can also stay in keeping with Dragon Ball's tone than those who are vastly more peripheral in the supporting cast. There's just a lot more to work with. It's not even close.
Anyway, again, none of this is to say that writing a story for Tenshinhan is impossible or forbidden. It just doesn't quite have the precedent that you think it does, nor is it some required obligation for a writer that moved him to the backest of backburners after just a couple of arcs in the 80's. As a character, there's really not all that much to him. Maybe they'll expand on him, but I wouldn't hold my breath.