A key quality of life improvement for me was to realise that you can eject the grounds from the filter funnel by putting the tube to your lips and blowing gently, ejecting the coffee puck into the food waste / compost bin. The Moka pot then becomes an almost zero-cleanup way of making coffee.
You need to do this after the pot has cooled enough that the aluminium won't burn your lips, but soon enough that the coffee grounds haven't continued to swell and wedge themselves in place.
This works similarly well with the Flair brand espresso maker filter cup -- though suggested nowhere in Flair's written or video instructions. Too undignified an act I suppose for prospective customers to imagine themselves performing every morning in future.
I've tapped to eject the spent puck for many years and it is not a problem. Maybe if you were aggressively whacking it against something much harder than the metal funnel it might become an issue, but against a hand or some soft plastic it's not an issue at all; there's been no change to the seal or shape.
I've seen that happen, but every time there was some other obstruction in addition to the coffee: popsicle sticks, silverware, pencils, etc. Usually something too long to make it around the trap. Those things will eventually glob up with hair or worse and clog the drain anyway.
In my experience if you wash grounds down the drain with plenty of water there's never any problem.
Another common myth among moka machine coffe drinker is that ground coffee is somehow "good" for your drains. I believed it naively until my landlord came and unclogged a ground coffee-filled drain.
You need to do this after the pot has cooled enough that the aluminium won't burn your lips, but soon enough that the coffee grounds haven't continued to swell and wedge themselves in place.