Nero being absorbed worked for the plot precisely because Nero needed an outside source of power to wake him up (Yamato) that wasn't with him when he was absorbed and could be given back to him at a moment's notice. For the plot to work the same way with Nero and Dante's places switched, it'd mean Dante has a similar connection to Yama, which he doesn't because it's not his sword, and an ability to restore it to an unbroken state, which he couldn't because it's not his sword. We don't have evidence he could do the same feat and it's presented as character-reliant: Nero's personality and arc was designed to be "Vergil With A Girlfriend". They both wanted power and were willing to send their humanity straight to Hell to do it, so they have an affinity to Yamato. Dante's in constant opposition to Vergil (literally, "[their] souls are at odds"), so their souls and their weapons don't resonate. Blah blah.
Alternately the plot would have to be that Rebellion is the Hellgate Sword (uniting both the Demon and Human worlds) and Nero keeps the Yamato on him and rocks around Fortuna with it (separating the Demon world from the Human world), gets the Rebellion over Agnus's dead body and gives it back to Dante, but that's suggesting Rebellion had any more power to give Dante before 5 went and did it, so there's no telling if anyone would buy that after Dante was impaled in 3 and got his DT and then got impaled in 4 to no effect, but, I dunno, fans bought DMC5's unintuitive "Seppuku For Sin DT" point fine, so that's a moot point.
So if Dante were absorbed, keeping everything else as-is. Nero probably wouldn't be able to save him, but Dante is presented as so absurdly OP by the point of 4 anyway that even if he got caught, he could have saved himself. What did Sanctus expect Credo, Nero, or Gloria to do, handcuff him? Ask him nicely? Have a whole pizza box lodged in one of the Savior's cores and a trail of slices leading the dude there? He had nothing that could draw him to the Savior to be caught -- evidently he didn't care that much about Sanctus having the Sparda sword, and neither did the game itself -- and Sanctus using Trish or Lady as a lure and then a meat shield to stop Dante from going all-out wouldn't have the same je ne sais quoi to it. He wouldn't get noticeably emotionally compromised seeing them in danger as Nero did Kyrie, or even as he was in 1 when Trish was held hostage by Mundus. He ain't that dude.
Overall it's too dumb a plot on Sanctus's part to argue in favor of it with anything close to good faith. Capcom tried to make Dante OP and emotionally unflappable to any villainous plot and that's their problem.