If the door is hollow, you may reveal the cavity inside, which I suppose could be filled in with wood filler. But I don’t think the result would be attractive. disregard, below commenter is correct, and was replying to this paragraph ^
Another aspect of this solution is that the door isn’t easily replaceable if it has to be planed like this. It’s no longer a rectangle. A replacement door would have to be modified too.
Right you are, I was thinking of the depth of the side pieces, not the thickness of the edge pieces.
Doing that could be fine for making more space at the bottom. It won’t fix how the gap is too big at the top. But if OP doesn’t mind, then no biggie.