It's certainly less important than the others, but I think it helps for being effective once in office; an incorruptible, competent, idealist without experience in government/politics would struggle to get anything done or would be influenced too easily by advisors. On the other hand, many times inaction by the government is far preferable to the alternative... You're certainly right that he or she shouldn't be too involved in the game or else we'd definitely be dealing with a swamp creature.
It's certainly less important than the others, but I think it helps for being effective once in office; an incorruptible, competent, idealist without experience in government/politics would struggle to get anything done or would be influenced too easily by advisors. On the other hand, many times inaction by the government is far preferable to the alternative... You're certainly right that he or she shouldn't be too involved in the game or else we'd definitely be dealing with a swamp creature.
Experienced in politics should not be considered a prerequisite.
It would be great for a candidate to be wise enough to navigate it, but you shouldn't have to be of it.