I own a bike with a big box in the front and parking has absolutely not been an issue for me. In the last six months I rode > 2600km in and around one of the densest European cities and parked in many different places. I have yet to find a place where I cannot park the bike . You can use regular car parking, but you will always find a dead corner, bike rack, big sidewalk, etc where you can leave the bike. And to be clear, I don't block the sidewalks or otherwise selfishly get in the way of other city dwellers.
My bike is an urban arrow, so one of the bigger two wheelers. ~7500€ new with all possible add-ons and a €150 annual insurance that covers the bike in full if ever stolen or damaged in an accident, so I also feel safe parking in rough areas with it.