How would making the few happier at the expense of the majority be increasing stability and reinforcing the status quo?

Very simple... it's literally recent history. FDR's New Deal (for instance) enriched the white working class and thereby separating it from the non-white working class, making any kind of class consciousness in the US very unlikely and preventing a repeat of the labor movements that rocked the imperialist nations in the aftermath of WW1 and the subsequent Influenza pandemic. The Apartheid-regime in South Africa essentially did the same thing without bothering with all the liberal propaganda.

It worked. In both states, it created a white "middle class" that was loyal to the status quo - you can witness that loyalty in it's full glory right here on lemmy.world. Neoliberals (as personified by Reagan and Thatcher) easily manipulated this loyalty to usher in the dismantling of New Deal-style Keynesian economics, leading to the deprivations you see in the US right now.