I think the main problem with this is I don't WANT my champion to be weak against armies.
Point taken. The champion is still stronger than an individual soldier, and an experienced one can probably take two or three soldiers down, more if the enemy is under-equipped (a champion knight in heavy armor can mow down enemy peasants with ease). And in battles the champion can act as force multiplier, taking out the enemy damage dealers, but being flanked by soldiers so that he can't be counter-attacked by too many enemies. But if the champion alone is always the answer, then the set of useful strategies is very limited.
With this approach, we can have:
1) A civilization that prioritized Warfare, and is fielding a large standing army of recruits. It's looking to bash some heads, but has trouble handling some of the bigger monsters wandering the wilderness.
2) A civilization that went Diplomacy and started taming monsters to defend against the first civilization's armies.
3) A civilization that prioritized Adventure, and has several high-level heroes with magical equipment, who explore lairs and advance it that way. The heroes have a chance of beating the standing army of first civilization, or they really help on defense (an archer hero behind walls can take out enemies with ease, whilst a general provides bonuses to soldiers). But they will find it difficult to take the fight on offense.