Without accounting, we can't tell where to divert resources to maintain or improve the equipment. It's also not possible to limit the use of the equipment beyond its stress limits without using money. Trains in particular require additional staff to handle high passenger loads. Some passenger trains are not set up to handle high traffic loads. Charging money limits the ridership to the people who want/need to use the train more than others. It also limits ridership of likely bad actors who will do things like key the windows or spray graffiti in the tunnels or on the trains themselves.
>Why would city spend significant resources to discourage usage of public transport?
Because then they would otherwise need to rely entirely upon the political process to maintain needed funding to the system, and there would be other spill-over impacts to the quality of the rail network.
>Do they really prefer for the people to buy cars and stand in traffic for hours on overcrowded streets and subsequently be disgruntled and pressure local governments for more roads?
I'm unfamiliar with road policy in Sweden. I imagine that the fares are paid through taxes on gasoline, tickets for driving violations, licensing fees for commercial vehicles, and other fees. The two transportation methods are not completely interchangeable. You can't run heavy freight on a passenger rail line. It's a bit easier to have shared freight and passenger traffic a highway. Expanding rail coverage to other regions is much more capital intensive than expanding road coverage, and much more challenging to estimate (see: the underutilized light rail projects all over the United States).
In a magical world of infinite resources and immortal human beings and infinite time, then there would be no reason to charge fees on anything. Because we live in a finite world of finite time and resources, we use money as a measurement tool to make better decisions with how we allocate our resources.
>Why only public traffic commuters pay if all benefit from the fact that they are not on the street crawling in 1.5 tonne of steel each?
Not all benefit at all times to the same degree. Also, it is probably also partially funded by taxes. That people are rebelling probably indicates other problems with the system outside the scope of the article.