I think, at best, it can only help with certain types of potential suicides. Some suicides occur due to apparently hopeless life situations. For instance, I haven't been able to get a real job in 23 years despite, in that time, finishing a B.A., an M.A., and a Ph.D. Nothing that everybody says to do works for me and I'm frankly tired of hearing it. I'm stuck DoorDashing (Uber was way too abusive) and that I'm stuck doing that is intensely depressing.
Psychology can't help with this. The only thing that can help is a real job. And that's what a lot of the babble about suicide prevention seems to miss.
You confuse the economic (neoliberalism) with a broader tendency of conservatism (neoconservatism), for which neoliberalism is a moral imperative. Neoconservatism holds that the U.S. political and economic system is the best system for all humans, regardless of history, regardless of culture, and demands that this system be "defended" at any cost, hence a muscular and imperialist foreign policy. Conservatism was the subject of my dissertation, so I do know something of which I speak.