The line class of rod doesn't dictate what size of fish you can catch - it simply makes the fight swifter or more drawn out e.g. if you catch a big fish on a light line class rod, you'll have to play the fish in more gently as the light rod can't bully the fish in quickly. But a light rod can absolutely handle bigger fish than the line's breaking strain. You simply set the clutch on his reel to give line at less than the b.s. of the line, so it never experiences enough force to break. Then you net the fish so that the line (and rod) doesn't take the strain of lifting a large fish out of water.
You need to think of the rod and reel as a system, rather than as individual items. A light rod, paired with a reel that has a properly set clutch can tame most fish.
The question then becomes one of fish welfare as it's one thing to be sporting but another altogether to be under-gunned and have to exhaust the fish (and Leo!) before netting it.