I'm typically running for my trains last-minute. Really, though, why should I have to do that? Isn't the point of a mobile boarding pass so that you don't need to do that?

I agree with diburning. The ticket should be scanned, you should get your seat check, and then you should be left alone for the rest of the trip (day or night). With the seat check, there is absolutely no reason to require re-checking tickets. (If crews can't read the other crews' seat checks, then Amtrak needs to standardize that.)