timppu: We have that "public TV tax" too in Finland, and those (YLE) channels don't have any commercials.
The commercial channels with ads are not financed through that tax, they are financed through the commercials.
As someone mentioned, one idea behind such national channels is that they are supposed to promote arts, education (e.g. learning programs, or documentaries even about "boring" subjects), services to minorities e.g. news for the deaf (I've never seen such on the commercial TV channels (not enough viewers I guess), albeit I am unsure how much deaf people nowadays need TV news with sign language when they could just as well read subtitles or read the news from internet, but maybe the sign language programs help them train their sign language skills then, and for hearing people too...), or news in the Saami minority language (the Laplanders living in the north) etc.
Commercial channels, on the other hand, concentrate more on stuff that gathers lots of viewers. Popular TV series, sports events, movies etc. Some of that stuff on the national channels too, but usually meant to somehow cater for the ideals mentioned above.
So I personally feel there is some justification for such tax-financed national TV channels, or nowadays also internet services. Some people complain that the programs on the national channels are not as interesting as on commercial channels, but those people completely miss the point. That's like complaining that going to school is not as much fun as staying home playing video games. It is not a popularity contest between the two.
The national (tax-financed) TV channels have a societal mission or purpose, while the commercial channels only have a purpose of making their owners as much money as possible. Both are needed, for different purposes.
receive money both from ad revenue and from a "subscription" which is the tax for using TV and Radio.