Sorry for the long delay everyone. I failed to mention a key point: I'd still brad or screw in the bottom along the sides. If not, as many of you have pointed out, the bottom would sag (especially when the depth is 17.5 inches).

I suppose dadoing along the entire box might make assembly easier. My only issue was that I've never done a dado before so I wanted to take a minimalist approach. But I guess if I'm able to do the front and back properly, I should be able to do the sides. I'm using a router table so it should be fairly straight forward.

And this is for my own kitchen - but my wife is an attentive customer haha.