You saw the thread title. Let's get one quick thing out of the way right upfront. This is NOT an Old School Kirk vs. Picard online debate from 1996. I had enough of those a long time ago. This is something else. In the Picard Series we have an older Picard where a significant amount of time has passed since the series and is in a different place than where we remembered him. In TWOK, we have an older Kirk (really just middle-aged but older relative to his age in TOS) where a significant amount of time has passed since the series and is in a different place than where we remembered him. I think in the Picard Series they can contrast Picard in The Later Years to Kirk in his Later Years. They can take a different approach to Picard than was done with Kirk. If Picard is someone successfully in a different stage of his life now, then he's been able to do something that Kirk couldn't. Picard was able to move on with his life. Kirk never did. When he was promoted to Admiral before TMP, he still wanted to be in command of the Enterprise. At the beginning of TWOK, again, he still wanted to be in command of the Enterprise. In TVH, they reward him with the Enterprise-A. He retires in TUC and it looks like this time it might be for real. But in GEN, he tells Picard since he retired he feels like he hasn't been making a difference and tells him not to let Starfleet do anything to take him away from the bridge of the Enterprise. Kirk never moved on. Clearly, if Picard's no longer in command of the Enterprise, something happened or he came to the conclusion that just because the Enterprise was Kirk's life doesn't mean that's all his life had to be. I think if they want the Picard Series to not be like the TOS Movies, and stand out as something different, then it's absolutely the right move to not have him resuming command of the Enterprise.
That's good, because it's the only question I ever thought was hard. The rest of that is an interesting observation, and I agree with it, BUT, I hope if they go the route you're suggesting, it doesn't preclude starships and starship combat from the series altogether. I'm a big fan of the ship porn and the pew pew.
Kirk was fundamentally someone who never grew up. Which is why the Peter Pan quote at the end of TUC was so apt. All he wanted to do was be out there in the big black and have adventures with his friends. Honestly it was such a terrible idea tacking on Generations because TUC was the perfect end to his arc, not being stuck in some sort of anomaly outside of time for nearly a century, only to have an underwhelming death scene. In contrast, Picard is the consummate Starfleet officer, and is already a "grown up" when we first meet him. While he certainly had an emotional attachment to his ship (and crew, as time wore on), you never really got the idea that he held anything higher than his duty, except in those rare circumstances where Starfleet itself didn't live up to its ideals and he found himself at odds with a particular admiral. I think he would willingly take a "desk admiral" job - but only if he thought it was in a role where he would be able to do as much to help Starfleet as captaining a ship - not as some sort of extended prelude to retirement. If Picard is going to retire, he will retire for reals, and just leave everything behind to engage his other passions (until and unless he is called back for some special mission).