This is a good summary. The other element is that Amtrak only gets priority if they stay to their schedule. They have a slot where they are expected, and have full priority. However, if they get delayed, and miss their slot, then another train will get in front of them, and then they're further delayed, etc., etc. The dispatchers can give them priority when there are two trains waiting to enter a segment, but that doesn't help if the segment is 90 miles long, Amtrak would run it in an hour at 90mph, but the freight train that left 20 minutes ago at 45mph is going to be in that segment for 2 hours total. Nothing Amtrak can do will allow it to be passed, especially if the freight is longer than any sidings that are available for enforcement.
Some additional enforcement might help, but in the end, with most of the network having large single-track sections, and the long trains of PSR, it's just not a network built for timeliness. About 50% of the train load in America is bulk commodities of one form or another (Coal, stone, grain, etc.) All of these commodities are generally stable and non-spoilable. Thus, the customers don't really care much about punctuality. A power plant can maintain some hours or days of inventory in a big pile next to the plant. If the train with the next load of coal is 8 hours late, it has little impact, you just dig a little deeper into the pile before it's refreshed. 8 hours is a big difference to passengers.
Is it impossible to expand the sidings? Maybe make them 5 miles long? Sure it's not free, but it doesn't seem like it should be outrageously expensive. Is this just classic underinvestment in infrastructure coming back to bite you in the butt?
Yeah, the main issue is mostly that the network is designed for lowest-cost, non-time-sensitive freight, and fast, time-sensitive Amtrak trains inevitably get stuck behind something slow, or waiting for something slow to clear from the other direction. A passenger-first network would look like Japan, with lots of double-track, few sharp turns, etc. It would cost more overall too.
Some additional enforcement might help, but in the end, with most of the network having large single-track sections, and the long trains of PSR, it's just not a network built for timeliness. About 50% of the train load in America is bulk commodities of one form or another (Coal, stone, grain, etc.) All of these commodities are generally stable and non-spoilable. Thus, the customers don't really care much about punctuality. A power plant can maintain some hours or days of inventory in a big pile next to the plant. If the train with the next load of coal is 8 hours late, it has little impact, you just dig a little deeper into the pile before it's refreshed. 8 hours is a big difference to passengers.