Unpopular opinion......
After the events of BOBW, Picard is the one who leaves, accepting the rank of admiral and sectorcommand. Enterprise is assigned to said sector, so we still have Picard in the show, with Riker in command of the Enterprise.
Or, Riker does leave the ship, but not the show. And setting up a show where we have two ships, interacting on occasion, with some episodes focused more on the Enterprise, some episodes focused more on Riker's ship.
Here's where the real world conflicts with the fictional one. In real life we know there's no way anyone involved with
TNG would want Patrick Stewart to leave at a time when
TNG was arguably at its most popular. Fans, certainly, would not have been happy to spend all summer anxiously awaiting the fate of Picard to see him shuffled off to a supporting role, akin to Admiral Ross in
DS9. Granted, you could have Picard choose the
Enterprise as his ship and have one of those (I'm in charge of larger scale missions, Riker, you're in charge of the day-to-day stuff). There could have been some minor conflict there as the two struggle with their respective roles. I just don't see that lasting the 4 seasons the show had left, though.
Dramatically, your idea is great, but practically, I just don't think it could have worked.
That being said, it seems odd to me that Starfleet didn't do more with Picard. You can claim that Troi helped him (in "Family" he says, "Counselor, your help has been invaluable during my recovery. I'm better... the injuries have healed..." and then tells her the nightmares are gone, granted the invasion might have been to blame, but we see them return in
First Conact), but we know it would not be enough. "I, Borg" and
First Contact (not to mention
Picard) show he has not fully recovered.
I just don't see how Starfleet didn't order him to headquarters for an intense psychological work-up and de-briefing session. I'm not an expert, but from the little I could find, returning POWs in the US undergo a long process of being re-acclimated to society and their previous lives. On one hand, yes, Picard wasn't captured for long. But the assimilation process effectively brainwashed him (not the best way of describing it, but I'm struggling for a modern equivalent). How did Starfleet Security think it was a good idea to just let him resume his regular duties?
I think more realistically, Starfleet would have held Picard for years to undergo psychological examinations, for one. Starfleet Security would have had to been 100% sure that the assimilation process did not leave them open to any potential vulnerabilities. Again,
First Contact shows us he still had some connection to the Borg and it's frankly amazing they didn't take advantage of that. Admiral Nechayev made it clear in "Descent" that Starfleet considered his decision to let Hugh go in "I, Borg" to be wrong. It's astounding they didn't consider it to be an after-effect of the assimilation and classified Picard as a possible security threat.
Then, whether Starfleet security itself or Section 31, someone would have been working the angle that Picard could be used as a weapon against the Borg. Certainly, he would object, but Starfleet hasn't shown themselves to be the type to put the needs of the one above the needs of the many.
Practically speaking, Picard should have been held at Starfleet for at least season 4. Maybe they promote him as a cover, maybe they're forthright that he's not going anywhere until he's been poked and prodded by every doctor, psychologist, and security official as needed to ensure (a) he's okay, (b) there are no lasting effects, and (c) he's not a danger to Starfleet and the Federation.
Riker, of course, would be promoted to captain of the
Enterprise, seeing as how it would have an open captaincy and he acquitted himself well during the Borg encounter. I'm not sure about Shelby being his XO. I think her work on the Borg would have kept her from serving on a starship long-term (unless Starfleet saw fit to give her a ship of her own to help with that work).
Again, none of this would work in real life, as I do't see Patrick Stewart leaving the show or taking a diminished role post the season 3 cliff-hanger made the show so popular.