But one thing that seems unavoidable is that the "section" (the part where you hold the pen) gets messy when you put the cap on it. I wonder why every fountain pen seems to have this design.

FYI, there are fountain pens with a retractable nib that don't have a cap, including for example the:

- Pilot Vanishing Point/Capless/Decimo (there's a cheaper Japanese "Special Alloy" version as well)

- LAMY dialog

- Platinum Curidas

I don't know if they fix your inky fingers issue but if taking the cap on and off is a hassle then these might be worth looking into.

EDIT: formatting