Yep, I too care a lot about Hoechlin's Supes, and would love to see him more than just in the periphery. I want to see more of his relationships to not just Lois and Kara, but also to the Danvers family (they were obviously close if he trusted them to raise his one living blood relative), Lex, Jimmy, Cat, Perry, etc. I certainly wouldn't mind seeing flashbacks to fill in some of that stuff from his past, either.
I don't see how that's feasible. One of the problems with the idiotic way the
Supergirl writers have approached their narrative is that they wrote Kara to be more like iconic Superman than unique in her own right. They've used so much of his cast and character traits with her instead of making her a teenager who is more alienated and science-oriented that its siphoned significant elements away from a possible Superman narrative. For instance, Hoechlin's cast of characters that you list include so many that are impossible to use.
Calista Flockhart and Mehcad Brooks don't seem interested in continuing in their roles, and both have had so much story told for them that have led them away from the center of the narrative. Cat doesn't work at The Daily Planet or even in journalism anymore, so even with Flockhart's unlikely interest in playing Cat again there isn't much chance her Cat and Hoechlin's Clark could cross paths. Jimmy, as far as I know, isn't well-liked by the audience and the actor is done with the part. Jimmy has also been the editor of a major media publication and is an outed vigilante. It seems unlikely he could ever return to Clark's life in any sort of traditional or meaningful way, and it doesn't seem like most people would be interested given how few fans his Jimmy has.
Perry and Clark rarely have any sort of meaningful relationship in any incarnation of the character. As for Kara, if she's busy on her own show or her show is over, I can't see Melissa Benoist reprising her role. Likewise, Dean Cain is not only toxic because of his political views, but his Jeremiah is in a very complicated place story-wise given we last saw him having seemingly betrayed the DEO and his family before disappearing.
Even more challenging is that the journalism-centric nature of the supporting cast doesn't lend itself to the CW superhero formula, as they aren't in a hub or lair of any kind and their skills don't really translate to the kind of team ups and set pieces shows like
Flash and
Arrow tend to do. Indeed, the CW's penchant for dropping the ball or complete disinterest in journalism stories suggests to me that they would struggle to create and sustain interest in that aspect of the Superman mythos. Also a challenge is the lack of villains. Lex Luthor is dead. Zod is dead. Corben's Metallo has already been confronted and defeated. Few interesting and compelling villains remain.
Since there are so many challenges to a spin-off that follows up on the current timeline of
Supergirl, only a prequel would make any sort of sense. That, however, has its own problems as the actors are mostly too old; they'd probably have to recast. So, at that point, why bother?