This is more nuanced. Some people in the government respect Barak. I don't know that Barak is active in politics (I haven't really heard him opine on the current government, but one can imagine he's not a fan). The more extreme parties in the government resent/oppose Barak. The "government" doesn't attack Barak or protest against him but certainly some (extreme/right-wing) political factions in Israel blame him for many things. I don't think he was sent because he's necessarily the best international law expert, but he's a very sharp and widely respected. His being sent while the government is trying to undermine the practices Barak established in the supreme court is a bit weird. Politics.