going by how much of the pagecount is given to the combat part of the game, it’s clear that fighting is supposed to be the primary mode of conflict resolution.

Combat tends to be rules-intensive, while social encounters are more abstract and DM/player driven. But there are plenty of pages in the rulebook dedicated to non-combat skills and powers. And I've played (and DM'd) games that are combat-lite. d20 systems work just fine.

Fighting is only the primary means of conflict resolution when the scenario is combat-focused. Survivalist, diplomacy-driven, and mystery/puzzler games tend to reserve combat as the consequences for initial failure rather than the first course of action.

I’m not saying you can’t have fun just solving things with freeform RP using D&D, but in that scenario, D&D itself won’t be contributing anything to the fun you’re having.

I played a Sherlock Holmes style murder mystery in which combat lasted a sum total of eight rounds for the full six hour session. The skill suit and class powers in D&D/PF gives you a wealth of non-combat gameplay mechanics, assuming you build with that style of play in mind.