Well to be fair, region locking makes sense.
Why should I, as a UK TV licence payer, fund programs for other people to watch?
Additionally, I believe that since the BBC co-producers shows with other broadcasters in other countries, the licensing agreements currently in place mean the BBC has to take steps to stop (for example) a co-Canadian produced drama appearing for free before it is shown in Canada.
Oh, and the BBC is not a state-run tv channel. It is a public broadcaster, but aside from the BBC Trust (which is more advisory), Government input is limited. Indeed the BBC have a very long and strong history of taking the Government (be it Tory or Labour) to task.
It should also be noted that there isn't a 'TV tax' in the UK. The TV licence is only payable if you actually own a TV capable of receiving BBC programming. Now whilst the licence system could use a bit of modernising, it isn't a blanket tax.