The reason this couldn't happen is because Vegeta lost control in the moment.
Super Saiyan 3 is a form based on control.
Still, to think he surpassed Goku in 3 from RAGE alone is impressive.
I actually think he's better off just snapping in this scene.
He loses either way but at least he hits harder in Super Saiyan 2 with the rage boost.
Kinda sad Daima is sorta stuck in it's own little continuity bubble for now.