Boolean and beveling 2 (related, but different)

I think there is something fundamental about boolean in Blender that I am not getting. In order to simplify troubleshooting, I am using 2 simple cubes.

step 1 boolean union. it created diagonal edges in top right and bottom left.

Just for fun, I tried to bevel the edge. See how it terminates in one corner.

I expected this, so I created another edge between the top left vertices on both cubes

But when I go to bevel, it still terminates in that corner.

The only way I can get it to work is to delete all the diagonal edges and build edges and faces from scrap.

I need to join a wing to a fuselage in another model, and rebuilding all the faces from scrap is a non-starter.

What am I missing? Blender’s boolean function is giving me headaches. Is it just fundamentally broken? Is there an add-on that works better?

(hopefully the pictures are clear. As a new user, I can only post 1 picture, so I had to photoshop them together)

Hi. Have you tried to merge the vertices? You may need to increase the tolerance so that they will collapse. I suspect that you might be seeing an open edge as the result of booleaning.