From an ideal mouse only workflow, I'd add two buttons right next to each other.

One that did another generate and than one that saved the current image on display.

That way there would be very little mouse movement between the two.

Though for myself I like using the space hotkey to generate new images, so only the toolbar button to export images.

For me my setup generates images so fast that I can more or less just tap generate until I see something I like. Which is why the automatically export doesn't work very well for me. I could see it being very useful for someone who had a slower system that wanted to pre-generate and save work to look through later.