Glue can be pretty strong when you've got plenty of area (like there), although unless you've got some diagonal bracing, it's going to be wobbly whatever fixing you use.
Most people don't use glue because it takes a while to dry, so you either run out of clamps after a couple of joints, or the clamps get in the way of the next thing. (by comparison you can bang in a few nails and call it done)
If you're worried about the screws rusting, use screws as clamps, and remove them after the glue has dried. Or leave them in and let them rust.