Do you think not being able to play 2-cost cards is not a significant downside?
Also, Jaraxxus summons a goddamn 6/6 with his hero power. You can't compare this shit to gaining 4 armor.
1) No. Obviously, it is not a significant downside. And before you ask, no, neither is restricting yourself to odd/even.
2) Are you intentionally ignoring their battle cries? Or the fact that it's 5 armor?