CA is brittle, wood glue is (relatively) flexible. Any wood joint using CA that’s going to see any shear force at all will most likely come very quickly. It’s sticks really well, but it’s not flexible enough to deal with wood movement, etc.
For gluing your cross in place, CA would be fine. That said, there’s no real reason not to use wood glue for it to guarantee a better bond, IMO.
Ryan/// ~sigh~ I blew up another bowl. Moke told me "I made the inside bigger than the outside".