No way this happens for multiple reasons.
First is the most obvious - Simmons doesn't want to play as a C at all ( , he doesn't even wanna play PF for that matter), and certainly won't take well to being traded and forced to bang with opposing centers all night long. That's a recipe for disaster, especially given Simmons' clear character concerns. Second - is Simmons at C really such an upgrade over Poeltl for the Spurs? Of course, the surface-level answer is "YES, absolutely!", but look closer - Simmons is as fatally flawed as Jakob shooting-wise, provides only marginally better defense than Jakob does (probably worse defense against Cs, which you don't really want out of your starting C), does provide the much better passing and transition game, and marginally better scoring (which as seen, you can't rely on). And on the other hand, he's owed something like $40M per year, for the next 4 seasons, compared to Jakob's measly $9M. Not enough of an upgrade in clear areas to justify such a big salary jump, IMO, especially when he'd be by and large the highest paid player on the Spurs.
Those are the big reasons, and also the ones I previously mentioned (Simmons' diva at ude probably turning off the Spurs' FO especially after Nephew fiasco, Spurs' uncertain future making the FO unwilling to part with future picks, especially the amount required to land BS, etc). I think the Spurs butting in as a third team to facilitate a Simmons trade isn't out of the table, but I definitely don't think we'd be getting Simmons in that deal, more like a pick and a bad salary from the team getting BS.