Why wouldn't you? Oh, is it because it wastes a day phase?
Town Governor is almost useless. What's the point in stopping a lynch the majority of players have agreed to? I'd have to be certain someone was Town and if that were the case then why would people be voting them? Plus players might just come back to it the following Day anyway. I could only really see it being useful if the game was in LYLO/MYLO and scum were obviously trying to force through a mis-lynch.