If the White Council got involved with national governments then they would be dragged into national issues. That could be bad. Very bad for council unity.
For example, if in 1914 the White Council had a good relationship with England/France/Germany/Austro-Hungary/ or Imperial Russia (or later: Italy, the Ottoman Empire, or the US) then their government contacts would be screaming "Help! We need magic to win this war. Look, we helped you with blah and blah - help us now!". And the White Council has enough problems staying out of that without owing favours.
Plus relationships would hamstring their work. For example, the events of Proven Guilty. Can you imagine them talking to a US government rep and saying:
"Oh by the way, there was this American citizen on American soil who was breaking laws that your country never passed, so we gave him a trial that didn't involve your legal system and then we executed him without allowing any appeals. Yes, we killed someone on US soil because we felt that was the right thing to do."
On the other hand, the US legal system isn't equipped to deal with warlocks - so the White Council has to do its job, but somehow I can't see governments taking something like that lying down.
Richard