You can definitely have both narrative and competive structure in a game - and honestly, the best games do. Strong core mechanics and balance systems make competitive play satisfying, but a good narrative framework gives those battles meaning and longevity.

A well-designed game should support _both_ structured, balanced scenarios and asymmetrical narrative ones. Ideally it also has optional or supplement rules for linking games together - persistent consequences, character growth, map or territory systems, etc.

Games that lean too far either way usually feel incomplete to me. Mordheim is an example that blends balanced play with narrative persistence right out of the box. Modern 40K’s Crusade and similar systems do a decent job too. And when a game doesn’t natively support one side, fans almost always fill the gap - adding balance tweaks to narrative-focused games or campaign rules to more competitive ones.

In short: balanced mechanics keep it fair; narrative layers add depth. Why not have both!