Actual use of this almost never happens, however.
This is because unlike other forms of transportation, railways are required to pay property taxes, so they're incentivized to have as little improved property as possible.
Minnesota does: https://www.revenue.state.mn.us/railroad-property-tax#
New Jersey does: https://www.state.nj.us/treasury/taxation/railroadtax.shtml
Missouri does: https://apps1.mo.gov/stcoriginalassessment/report/CompanyRep...
The problem was so bad at one point that one of the steps taken to arrest the rail industry's decline was to ban property tax discrimination against railroads: https://www.thetaxadviser.com/issues/2014/dec/tax-clinic-10....
You never see this in Amtrak discussions, because Amtrak does not own the vast majority of the rails it runs on, and people couldn't care less about private companies. For highways and airports, they're pretty much all on publicly owned land, so they don't pay property tax because that would be silly.
And your 10 minute plan gets complicated when you consider they pick up passengers at multiple stops along the way. If they waited an extra 10 minutes at every stop they might ending up causing themselves an even bigger delay.
But I don't have specific info on what things are causing the most delays.
The is because Amtrak must share lines with much slower cargo trains.
Amtrak will file for "track windows" where they have exclusive access to the track for higher speed travel - but if they miss the window (for example a passenger had luggage trouble and delayed the train by a few minutes) then they are stuck behind cargo trains.
And once that happens they have no way to recover their original time table. The train will be late all the way to the final destination! And not just a little late, travel time will double.
I'm not aware of any good solution for this.