Can you imagine what our Interstate Highway system would look like today if it was developed only along existing ROWs. They would be at least as goofy as the Northern and Southern State Parkways on LI if not considerably worse.
Not sure how it is everywhere else, but in Alabama almost all of I-20 is made up of the ROWs of state, federal and local highways. In some areas we have a sign with I-20, I-59, US 78, US 11 and AL 5 all on one ROW. Apparently one was built first and as the others were built they shared the ROW ending with the interstates.
You are wrong about I-20 in Alabama. It was built almost entirely on new right-of-way. East of Birmingham it parallels US 78, which has its own ROW except for just west of Pell City where I-20 must have needed to us US 78's ROW for 3 miles. West of Birmingham, I-20/59 parallels US 11. They only share a ROW for about 10 miles.
In the eastern US, the generally the Interstates had all-new ROW, separate from the US highways they usually paralleled. This was because the US highways had a lot of development along them, even between cities/towns, and the cities/towns were close together. So re-using the old ROW would have been expensive because of relocating all those buildings.
In the western US, many of the Interstates were built on existing US highway ROW because there was little development on them in rural areas and the towns were very spread out. But many of the western Interstates were still built on new ROW too.
Generally speaking, if there is a state route co-signed on an Interstate, it was to move the state highway traffic to a better highway. In the case of AL 5 and AL 7, they already followed US 11 west of Birmingham, and so when I-20/59 came along and took over those 10 miles of US 11's ROW, AL 5 and AL 7 also followed.
Also look at I-65 in Alabama. It parallels US 31, but very rarely do they share a ROW.