Back to the original question:
Most of amtrak runs are on single track railroads because most railroads in the US are single track. It is really that simple. Outside the northeast corridor and a few other short sections, most of the tracks that Amtrak runs on are owned by freight railroads. With the drop in train miles after WW2 and cost squeeze in many other ways, and availability of improved signaling many formrely double track lines were singled in the 50's, 60's, and 70's. Only since the mid 1990's has traffic volume reached the point that conversion of double to single generally stopped and instead second tracks and additional sidings are being installed.
A few lines by route:
Lakeshore Limited: mostly or all double track. However, this was a four track main into the 50's.
East coast service:
Washington to Richmond: double track - has been for years.
Richmond to Jacksonville via Florence SC (A line) converted from double track to alternating single double or single with long passing sidings in the 70's and 80's.
Raleigh to Savannah via Columbia SC (S line) single and always has been.
South of Jacksonville: all have always been single. Some short segments of double on the A line. West Palm to Miami doulbling is new.
Crescent Route: Washington to Atlanta: used to be double, converted to alternating single and double in the 60's. South of Atlanta, always single.
City of New Orleans: All single. Was double until late 80's Chicago to Cairo, Fulton to Memphis, and Jackson MS to Hammond LA.
Sunset Route: Always single, except about 75 miles. UP now doubling all west of El Paso.
Southwest Chief Route: almost no change of passenger route over last 100 years. Double Chicago to west of Kansas City. passenger route through Topeka is single, passenger route across Kansas and Colorado to just beyond Albuquerque is single, from there west it is double the rest of the way.
Anyhow, I how you get the idea.
George