Lots of good replies so far, but no one has pointed you at https://www.nps.gov/subjects/nationaltrailssystem/index.htm for the so-called National Trails System which encompasses National Scenic Trails, National Historic Trails and National Recreational Trails. As pointed out by others, many of these are (intentionally) not anywhere close to civilization for most of their lengths, are quite long and rugged, but some are clearly East-West.
However, I would not be daunted by trail difficulty. If I wanted to walk across the US, and not walk along old highways, I believe I would look seriously at "The Great American Rail-Trail", https://gis.railstotrails.org/grtamerican/. As mostly former rail routing, it tends to have gentle sloping and does go through towns every so often. Sadly it is not yet complete, with large gaps in Wyoming and Montana. On the other hand, large complete segments such as Washington DC to Pittsburgh seem ready for someone who can do 300 miles on foot or bike. If you don't mind small gaps, you can get almost to Chicago before having a gap exceeding 25 miles.
Good luck, and if you decide to try a journey, please come back to the Forum and tell us all about it. It will be quite interesting I'm sure.