Yes, coffee equipment is best rinsed. Mokka pots even explicitly instruct you not to use soap and let the residues build to mask any potential flavor from the metal.

I think that's specifically for aluminum moka pots. If you've got a stainless steel model, you can wash it properly without fear iirc.

Meanwhile, I'm seeing ads from Nespresso with catchphrases such as “Did you know aluminum makes your coffee even tastier?”.