I contacted Lys Burden, the principal designer of the TransAm Trail back in the mid-1970s. Here's what she has to say:
The TransAm Trail was launched as a bicentennial project and focused on history as much as geography and suitable backroads for bicycling. The original west coast teminus was Reedsport, Oregon, but the trail was extended to the north to end at Astoria, to include, celebrate and honor the end point of Lewis and Clark's expedition. We looked for an equally historically significant and "off-the-beaten-path" place for the east coast terminus, and the historic triangle of Williamsburg, Jamestown and Yorktown seemed like the perfect place. We also had to factor in the total length of the trail, as we were trying to keep it in the vicinity of 4,000 miles. We reasoned that if it became too long, cyclists would not be able to complete it during a "summer vacation" time period.
Also as the route approached the east coast there were not too many viable options to find a good, continuous route of backroads all the way to the Atlantic Ocean. We had to make regional decisions as far west as the Cumberland Plateau in Kentucky. We decided to cross the Appalachians at a narrow spot and take the trail parallel to the trend of the mountains to the north through Charlottesville (to include Thomas Jefferson's home at Monticello) and make an expedited crossing of the piedmont. To make a bee-line for the Atlantic, the trail would have to head straight east from Blacksburg, Virginia, through an endless expanse of piedmont hills, with not too many noteworthy or historic places... to end somewhere near Virginia Beach.