I still think you don't actually grasp what 'face' is in Chinese culture. It's actually strong enough socially to be considered "power and influence". To China, the US sticking with the One China policy is considered a gesture of goodwill, and therefore the US keeping to this policy is giving the US power and influence when it comes to relations with China.
Moreover, you mistake that it's up to outside nations (aka the US, the rest of the world) to determine whether or not China should have the One China policy or not. The US recognizing Taiwan as an independent nation does not change either China's or Taiwan's positions on being the 'proper' China. The reason Chinese people want a Unified China has to do with their long, long history dating back to the Spring and Autumn Period where the people of the land spent hundreds of years fighting endless wars with each other. China's history means they can't be a Europe where the countries separated after the Roman Empire and learned to live with each other (Europe still had a shitton of wars, including the two worst in history). China's history means their people want to be One China, because the ideas of peace and prosperity are closely associated with times in history where 'China' was unified as one.
From a US perspective, the policy regarding Taiwan's status buys time. Yes, it is not adherent to the lofty ideals of democracy. But from the very beginning of US history when the Americans decided not to assist the revolutionists in France shortly after the American Revolution, we were not adhering to those ideals in the foreign theater anyway. The juggle between China and Taiwan is intended to give time for China to develop the government from an technocratic oligarchy, to develop the populace into a more educated, demanding one—to get time for the societal, cultural, political, and economic changes to take root to the point where China may eventually be more sensible about Taiwan.
Because of the lack of a credible higher authority, the international stage is not a place to play with principles and morals.