completely" is not the relevant metric, IMO.
Yet the word is the only relevant one for when horses, as a whole, were replaced by machines. The cities themselves were not the "benchmark" for the automobile takeover because they were historically more suitable for a car than a horse . Horses required a huge amount of infrastructure - feed transport, stabling, manure disposal, shoeing, harness making and repair, wheelwrights, carriage makers and repair, stable hands, coachmen, and veterinarians - that cost vastly more in the long term than an automobile. Space itself was at a premium in the cities and only the wealthy could afford the keeping of one or more horses next to the owners' homes. So when the car tootled onto the scene, with very little required to keep it, no cleanup, no fuel unless it was used, it was a godsend for anyone living in the city. Now tradesmen didn't have to hire out horses from a livery stable (which was were the vast majority of working horses came from) but could buy a truck and keep it parked out on the street for whenever they needed it. Less staff and far less work plus greater comfort and safety since cars didn't spook, shy, bolt, or fall over dead while still in harness. Plus anyone could drive a car, technically speaking. The roads were already paved in most cities by the 1900s which was another selling point for the car. It was smoothing riding, could go long distances without tiring, and so much simpler. They were the true universal tool.
So the car quickly became the darling of the city dweller by the first decade of the 20th century.
But just beyond the city limits were the endless interstate network of dirt and mud roads, the at grade fords for stream and river crossing, hideous ruts in the wet season and slippery conditions in the winter where 4 hooves were so much more efficient and trustworthy. The height of the horse and the wagon/carriages made horse drawn transportation much more reliable when road conditions were poor or non-existent. Horses could be fueled by free grass and water alongside the road, and there were extensive networks of farrier/carriage repair/overnight livery stables everywhere in the countryside.
It actually did take decades for the car to inch it's way into the countryside advancing only has fast as the road/bridges/fueling supply infrastructure was built to support the new wheeled transport. Trains were still favored for freight and long distance, and canals where there was a continuous river network, but horses remained with the local farming communities until Eisenhower signed into law the interstate highway system. That billl finally rang the death knell for horse drawn transportation everywhere. It kinda rang the bell for the railroad as well.
BTW - Neither of those old photos were of any "Easter Parade". They were snapshots of daily life and congestion in a city.