What kind of argument is this? Mostly pedestrian, public transport and bicycle based cities still have utility trucks and vans which you can use when you really need to. It’s a pain to navigate the city and the parking fees are high, but it’s something you would totally accept to for moving homes.
You can try googling “How to move homes in Amsterdam” and see whether people there manage to move homes.
TLDR: It’s not black and white, nobody wants to prohibit EVERY SINGLE MOTORIZED VEHICLE FOR EVERY SINGLE USECASE.