Depends on the government. Poland for example was ok with criticising the government on the national tv for many years, until the last swing to "law and order".

So there are no guarantees even if it works without censorship currently.

("law and order" means PiS, the previous rolling party) I think this is the biggest issue - the temptation and the power to take over the national media is always there, and all it takes to dismantle all the checks and balances is one determined filling party.

In the other hand, the US manages to control it's completely privatized media, so maybe being publically funded is not the issue.