Screwless towel hook for bathroom cabinet mirror (DEATH TO THE STUPID SUCTION CUP HOOK)

So we use a suction cup hook in the bathroom instead of drilling yet more holes into the wall.

I read I should use hairspray so it sticks better.

I have to pic it up every two weeks or so.
And it makes a ugly spot onto the tiles.

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Why didn't I think of using my 3D printer earlier to finally fix this issue?
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One of the images is the side view of our Ikea bath mirror cabinet. It rests against a ceramic tile backsplash.
The wood frame of the cabinet is ~1.2mm thick, and so th