consider it like a library, the TV stations that get the license are required to produce and broadcast information to the public, cover important national events etc. and can do so without having to cater to advertisers and such
For Germany, the radio "tax" is intended to allow for a production and broadcast of politically neutral and informative program. However a huge part of that gigantic pile of money is now used for paying absurdly high pensions, even though the "tax" grows ever so often, the money used on the program is reduced on a regular base. Currently, the demanded rise in "tax payment" has been declined by state officials (I think for the first time in history), nevertheless the public broadcasters will receive their raise - they will take legal action against the expressed public and politic will, and they will succeed.
And: Of course the public broadcasters make excessive use of hidden and plain advertisement.
Good thing is, you can watch it in Danmark, for free. While we simply cannot watch danish TV, just across the border, even with the kids visiting the danish school. No, there is no way to obtain the required viewing accoung (unless someone "lends" it to you).