(Sometimes, there are uneducated politicians that get voted in due to popularity, like celebrities.)
In my country
mostly the uneducated ones get into higher politics because they are usually very good on making friends where they need and they can unscrupulously blackmail other politicians and bribe voters.
Also many are part of the old communist party or descendants of those members.
Celebrities do have a chance too, but most stay away.
And governments probably don't want to risk having to control a highly educated population...
Not probably, certainly. They prefer people they can easily lie/manipulate, people who usually forget that there are the same lies every 4 years.
The ones who think before voting are dangerous are are heavily discouraged.
Remember, the main goal of a politician is usually to keep his "job" over and over again.