I'm curious what country you're from to have that point of view. In the US the public radio is extremely clearly not a state sanctioned propaganda; some of the corresponding private news corps are much more.
I live in the UK, and the BBC is definitely propaganda.
I also agree with you that private broadcasters can definitely be worse.
OTOH, it's a vicious circle: you cannot fix society without fixing propaganda, and if the propaganda is any good, you cannot fix propaganda without fixing society (most people will lend an ear to it, believe it, parrot it, support it, work for it, etc.)... so we just have to learn to live with it :/
Are you sure you know what "public broadcasting" is? It's broadcasting funded by the public, mostly through private donations and some funding through competitive grants.
EDIT: I see from your profile you're not in the US, which is probably the source of the confusion. Examples of Public Broadcasting are https://www.npr.org and https://www.pbs.org.
As a US citizen who used to listen to NPR daily, it may not be state-sanctioned, but it definitely had a propagandistic narrative tying together the reporting.
Maybe not quite as strongly so as the NYT, but it was definitely there.