I think the “spreading democracy” mindset is wholly unsubstantiated, as most of the wars you mentioned were predicated on either preserving or spreading democracy. If we need war to prevent war, it seems that there can be no peace.
As anyone who's ever had a war fought on their soil will tell you.
When was the last time a war has been fought on your country's soil? How many times since then has your country brought war to another's?
Your opinion might change were you on the receiving end of these adventures.
This statement remains unsubstantiated, and is furthermore argued against by the wars originally provided in the general context of the quote.
But no, even with authoritarian regimes in existence, there is a difference between "shooting war" and "no shooting war". That difference matters, too.
As far as preventing war in general, the Korean War, Vietnam, Soviet invasion of Afghanistan, the Falklands, two gulf wars, Russian invasion of Ukraine, etc, etc. UN mediation is no more effective than any other major power mediation efforts in history, in fact it can be argued the UN has been less effective.
The key method to avoiding war is to spread democracy, which is why the UN is such a failure, and it’s charter is the prime reason.