You're being unrealistic.
I live in a large apartment development in Manhattan that is pedestrian-friendly and decidedly vehicle-unfriendly. You can't drive a car to the front of my building. And yet it works, very well.
I moved in with my girlfriend recently. You know how that worked? The movers she hired drove as near as possible, and simply pushed her stuff on dollies the rest of the way to the building. No big deal. Yeah, it took a little bit longer, but nowhere near as bad as the 4-day move you're hyperbolically claiming. And that side of the move was actually better than the other side, since she was moving out of a fourth floor walkup. Even though the truck could park almost directly in front of that building, it turns out it's harder to carry stuff down many flights of stairs than it is to push it on wheels across a flat surface and then up an elevator.
I moved from another building within my complex, and I accomplished my entire move simply by pushing my stuff on a dolly, without even having to hire movers. I've never before had a vehicle-less move even be an option, but it was in this situation.
As for repairmen, you know how they work? They get around on bicycles. You can carry a surprising amount of stuff on a bicycle, including all the tools you'd need for >95% of repairs. The plumbers ride around on bikes with a toolbox, plungers, and a snake, for example. For appliance delivery, they use tiny little vehicles that are basically a pick-up truck version of a golf cart. These vehicles don't go fast and the drivers yield to pedestrians, and you see them on pedestrian paths (and don't feel unsafe about it).
Every problem that you're bringing up is already solved in the many different areas that are pedestrianized and prohibit vehicle traffic. It's a failure of imagination to think that these problems are unsolvable. When your city is dense enough, a plumber/electrician can easily support him/herself on just jobs that are within a 10 minute walking radius, with the tools that can be pushed on a handcart or fit on a bicycle. Vehicles aren't necessary. It's actually more efficient for these professions, because in the suburbs it's typical to drive for up to an hour to get to a jobsite! So much wasted time spent just getting somewhere!