Fuel was definitely an issue, but you could just carry tins of fuel and the car wouldn’t mind carrying them. Carrying food and water for a horse is no joke, and horses also need to rest. You also don’t have to take the saddle and bridle off a car, wash the car and brush it down. Horses really are a lot of work, especially if you’re working them hard. Remember that work also comes at the end of a long day in the saddle, which is hard work for you, especially if you’re beating a trail at a trot.
Parking... I have no idea about the logistics of parking at that time, so I can’t say.
> At the turn of the 20th century, the most malodorous environmental challenge facing the world’s big cities was not slums, sewage or soot; it was horse dung. In London in 1900, an estimated 300,000 horses pulled cabs and omnibuses, as well as carts, drays and haywains, leaving a swamp of manure in their wake. The citizens of New York, which was home to 100,000 horses, suffered the same blight; they had to navigate rivers of muck when it rained, and fly-infested dungheaps when the sun shone. At the first international urban-planning conference, held in New York in 1898, manure was at the top of the agenda. No remedies could be found, and the disappointed delegates returned home a week early. (https://www.economist.com/special-report/2016/11/26/the-futu...)
See also The Horse & the Urban Environment: https://enviroliteracy.org/environment-society/transportatio...
That said, I'm unconvinced that smell and mess are as compelling a selling-point as all that. Societally they're very important, but not obviously more than non-fuel-burning vehicles today. In practice, when it comes to making a purchase, there are often much more pressing concerns than an environmental issue over which you individually have little influence.
Cars could only travel on roads, you couldn't go wherever you liked as on a horse. Narrow passages you could previously have ridden down were now inaccessible.
You need to put fuel in your car, which was probably even harder then than finding an electric car charger at the start of their existence. Providing food and drink for a horse was comparatively trivial.
Horses could easily be tied up outside of whatever store or destination you were visiting. What were the social costs of parking a great big machine outside of your local? To say nothing of parking as a town- or city-wide logistical problem.