Schedule padding is all about perception.
From the travelling public standpoint, a train that arrives on time is a "good", consistently-timed train. Most passengers look only at the arrival at their destination time, be it the end-of-the-line or somewhere in the middle. Hence, padding injected all along the route...5 mins here, 10 mins there, etc. As a result, trains have to "wait time" (eg, they arrived early) at some stations so they depart on schedule. Many passengers don't understand that the train can't leave early (except at discharge-only stations) and frequently ask: "why are we just standing here?" Arriving on-time facilitates everything from cabs to family arriving without too much waiting to meet up with the arriving passenger(s). As an aside, back in the "earlier days" of Amtrak, rolling into a station 6-10 hours late, I routinely heard: "I'll NEVER take the train again!!!". Just listen in the airport sometime when a plane arrives even 30 minutes late! Never mind that there were tornadoes in the vicinity, etc....IT WAS LATE!!! That's ALL they remember about the journey.
From the perspective of railroad management, be it Amtrak or one of the host railroads, consistent on time performance is good for at least a couple of 'atta boys'....maybe even a promotion! It doesn't matter HOW the manager succeeded in getting the train to run (usually) on time. Running on time also facilitates the 'slot' mentality for scheduling, so that, with routine, dispatchers can set up meets and passes at "the usual" locations, etc. In short, running on time keeps the railroad fluid. But then, there's the busted air hose, a dumb motorist (Darwin candidate), or SOMETHING to mess up a nice schedule!
And lastly, from the perspective of Congress, arriving at the end-point city on-time is a measureable statistic that "they" base their decisions (votes) upon. How many trains would Amtrak have today if the perception was "never on time" (like a recently merged out of existence airline I used to fly 30 years ago). Think about it.
It's all about "looking good" to whomever is "looking" at you. If its transportation, on-time performance is one of the biggest things "they" look at. Another common transportation measurement is how many dollars per mile, or per passenger, or ton of freight, or....<whatever>. It's simple and it's measureable. That's the two most important factors in every business today. Never mind quality, eg, was it comfortable?, or did the product last a long time. Unit cost, profit, and measureable consistency is what it's all about. In terms of Amtrak, happy customers come back, unhappy customers don't. The same is true of all passenger transportation enterprises.