As an equal marriage (and general civil rights) proponent, I think it's less that "the process works" and more that we have gotten very lucky that the Supreme Court has accumulated far more power than it was ever intended to have and has largely used that power to override the democratic will of the majority in cases where it has been oppressive to various minority groups. If we had to wait for the "right" laws to pass through legislatures, I don't believe we would have nearly the level of civil rights that we do today.
I think the courts and bureaucracy being unresponsive to popular opinion, social norms (social stare decisis if you will), and the regular rules of American democracy (i.e., actually amending the Constitution when appropriate) has resulted in the rising popularity of figures like Donald Trump.
It's hard to argue that the system isn't rigged when the rules of the system aren't as important as the outcome that relatively powerful decision-makers want to see.
I agree with you that populist movements are a natural result of systems like ours that are not fully democratic. Whether or not you think the system is "rigged" depends on what you think the system is. If "the system" is the form of government we've had since at least the end of the civil war (but really, since close to the beginning), with a strong non-representative bureaucracy, a powerful judiciary, and powerful private political parties, then it isn't "rigged", it just has components that don't answer directly to the people at large. But if you think "the system" is a pure democracy, then yes, it has been "rigged" from the start. Personally, I'm a much bigger fan of our system with all its checks and balances between competing interests than I would be of the more democratic system that a lot of people seem to think we have.
