I don't know about permanently, depending on how this all shakes out in the end. But there is definitely a reason why Sony is not signing the 10-year CoD deal with Microsoft. That's because Sony knows they are virtually guaranteed that much anyway. Even without a deal. All three regulators want some kind of concession, if they're not trying to outright block the deal. Like the FTC. And thus far none of them have given any signal that they're okay with no concessions at all now.
If Sony signs a deal, they give Microsoft a lot more leverage to argue the regulators. What Sony is trying to do now is see what the regulators are going to require even beyond CoD being on competing platforms for many years to come. Sony's desire, clearly, is to see the deal killed entirely. Now, they probably would have been plenty happy just to see Microsoft forced to divest Call of Duty and the studios associated with it. Which the CMA outlined as the weakest structural remedy they would accept. The stronger two being complete divestment of all of Activision or complete divestment of both Activision and Blizzard.
The CMA has said they don't think behavioral remedies will be sufficient, though they have not yet 100% ruled them out. However, the chance is small. If Microsoft is dead serious about walking away from the deal if they have to give up CoD, then that means the CMA alone has made it likely the deal is dead. So, between pretty much being certain that they're going to be getting CoD for a long time to come, and now Microsoft saying it's all-or-nothing for ownership in regards to the structural remedies the CMA has said they'd prefer, Sony would be absolute fools to sign anything now.
This doesn't even touch on the FTC. Even if they could be convinced to not outright block the deal, they're not suddenly going to be okay with some 10-year CoD deal. They're going to want a lot more than that. Likely the same kind of concessions the CMA has suggested thus far. But the FTC is out to make a point so good luck getting them to shift on this. Microsoft will almost certainly have to take them to a higher court and then hope the judge not only says they can buy ABK but doesn't also demand divestment.
The FTC alone could keep this deal contested until 2025. Since that's the earliest the current leadership could be changed, and their course reversed, if a different president is elected. And if not, it could take even longer than that for a higher court to get to the case and make a decision. That's also if the EC or CMA, in the meantime, don't demand something that makes Microsoft walk away like they claim.