As far as on time I don't think the day matters.
Amtrak doesn't own the tracks or track infrastructure and is at the mercy of the track owner dispatchers and repair crews if track infrastructure causes a delay.
Plus weather, idiots trespassing on the ROW or ignoring grade crossing warnings/mechanicals and getting hit by the train, and Amtrak rolling stock problems all can make the train late.
My sister was recently on the California Zephyr. On her return trip from Reno someone on the train had a medical emergency, and later one of the 2 locomotives broke down so she was 6 hours late getting back.
But she's like me and figures that extra 6 hours was a bonus extra dining car meal and 6 more enjoyable hours on the train at no additional charge.
If you have a tight schedule and have to be in Flagstaff by a certain time you might want to consider flying instead of taking the train.