What is public television? Europe vs United States

It is difficult to explain European public TV to American media specialists. They don't get it. PBS, the American public television, is a different business model, completely. What can be learned from a comparison?

According to a recent survey, PBS is the most trusted American institution. PBS is trusted for its news and public affairs programming. More trustworthy than the federal government, the courts of law or even Congress. Only the nation's military defense institution does better.
Of course, other media (digital platforms, cable and satellite channels, broadcast commercial networks) are far behind. PBS Kids is praised for its great educational value, outranking Disney or Universal Kids.

PBS is a network of public TV stations: it is, therefore, both national and local thanks to its 350 member stations.
PBS is free for consumers: nevertheless, they can elect to support their local stations through donations or even participate actively (volunteering). There is no yearly tax (no "redevance" as this tax is called in France, where a tax must be paid by any household with a TV set: 139 € / year (i.e. 158 $). 13$ a month: more than the price of a Netflix subscription!
Of course, PBS airs no mass entertainment such as football, baseball or car racing, leaving these to the commercial networks. When hearing about European public TV, Americans ask: tax money for sports retransmissions? How strange! If sport belongs to entertainment it is consequently a matter of individual choice and budget (cord-cutting in the US shows that not all people are ready to pay for sports programming).
And there are no commercials on PBS whereas most European public TV channels air commercials; PBS carries only sponsorship, discreet underwriting,  considered favorably by companies since a PBS partnership is good for their image.
That is why 30% of American people trust PBS compared to 13% who trust commercial broadcast TV or 8% who trust the newspapers. PBS can boast that it is "America's Largest Classroom, the Nation's Largest Stage and a Trusted Window to the World".

Survey developed by PBS, conducted online within the United States, by M&RR, January 3-8, 2019
Sample: 1,015 adults ages 18 and older (495 men and 530 women).
Results weighted to be nationally representative of the U.S. adult population.

Why are there so many public channels in Europe, channels which most of the time imitate or follow commercial channels? Public television in Europe is often nothing but State-run commercial television (with at least two noticeable exceptions, the French-German ARTE, and the BBC in the UK).

Now that the Internet carries thousands of programs, does a developed country still need public television to air the same kind of programs as commercial TV channels?
After education, what are nowadays the most important tasks of the State when it comes to culture and communication?
Once there is no "digital divide" (we are not there yet), once everybody will be able to access the web and the services it carries (a question of training to be solved), what becomes of public television's purpose? Such a question belongs clearly in the tax debate.