Within Virginia, the investment in a canal was an investment in just one portion of Virginia. Because river improvements would benefit just a narrow group of people, proposals for public investments in specific canals stimulated sectional rivalries. Public funds spent on the Potomac did nothing to reduce transportation costs in the middle of the state; why should Nelson County taxpayers support a canal that would benefit farmers in Loudoun?
The Dismal Swamp canal benefited Norfolk, Portsmouth, and Suffolk - and did little for any other part of Virginia. The upstream residents of the James River valley, and especially the citizens of Richmond, would be the primary beneficiaries of a canal around the falls at Richmond.
Similarly, residents in Culpeper, Orange, and other upstream counties - and of course Fredericksburg - would gain advantages from transportation improvements along the Rappahannock River, while enhancements to the Appomattox River would benefit Petersburg and the upstream residents in that watershed. The upstream residents in the Potomac River valley, plus the residents in Georgetown and Alexandria, would benefit from a canal around the Great Falls on the Potomac.
The main rivalry in Virginia was between the Potomac River and the James River watersheds. The Potowmac Canal and the later Chesapeake and Ohio (C&O) Canal in the Potoma watershed helped farmers in the lower Shenandoah Valley and the merchants of Alexandria - but took potential business away from Richmond. The James River Company and the later James River and Kanawha Canal in the James River watershed provided no economic benefits directly to Virginians along the Potomac River.

Not surprisingly, the General Assembly initially balanced its investments in the two canals. George Washington was an advocate for the Potomac River connection with the Ohio River, but he too felt obliged to express support for improving the James. The answer, of course, was to propose simultaneous improvements to the James and the Potomac regions. This would create a sufficient coalition to overcome resistance from others regions that would gain nothing, such as Tidewater plantations that already had easy access to transatlantic shipping.
At the same time, however, George Washington dreamed of the Chesapeake and Ohio Canal and other such projects uniting different sections. Washington and others viewed canals as essential transportation improvements not only for reducing shipping costs for farmers east of the Alleghenies, but also for facilitating trading alliances across the Appalachian Mountains to ensure western settlers were economically connected to the Atlantic port cities.
Trade between the Ohio River and Atlantic watersheds would facilitate political alliances and peaceful resolution of conflicts. This is still a viable argument, though the locations have changed - listen to the debates for permitting sale of American wheat and corn (and even software and high-tech items) to "rogue countries," for supporting the World Trade Organization, for expanding the North American Free Trade Alliance (NAFTA), and for ending sanctions against so-called terrorist states...
225 years ago, George Washington feared that settlers in the Mississippi drainage would have minimal economic ties to the east coast. France and Spain claimed dominion in the Ohio River watershed by right of prior discovery - to the French, Louisiana extended far up the Mississippi and La Virgine was east of the Alleghenies. Their foreign military post at New Orleans controlled Ohio River trade, since water transport was the most economical way to carry surplus products from farm to market. The British colonies along the Atlantic seaboard (and later the new country called the United States of America) might be limited to those lands east of the mountains.
The risk was real. In the early 1800's, the head of the United States Army schemed to steer the allegiance of western settlers to Spain and away from the United States - and former Vice President Aaron Burr was tried in Richmond for treason related to his similar efforts.
Virginia was the dominant member of the new United States from 1775-1800, with more people and a stronger economy than Pennsylvania or New York. However, in Pennsylvania the Schuylkill and Susquehanna Canal bypassed the Great Falls on the lower Susquehanna River in 1797, and in 1803 the Chesapeake and Delaware Canal was started to connect Philadelphia with the northern end of the Chesapeake Bay. In New York, the Erie Canal connected the Hudson River valley with the Great Lakes in 1825, and by 1840 New York was the preeminent state in population and economic power. Virginia politicians mourned the decline of the state's importance and the state's residents continued to emigrate to new lands on the frontier, while Virginia floundered in its efforts to establish cheap transportation connections with the Ohio River.
In the "what if?" category, imagine how Virginia might have evolved if the Potomac River or James River canal initiatives had been successful in reaching the Ohio River. Virginia might have retained its economic leadership - and the Civil War might have been averted. Though the Northwest Ordinance barred slavery from the territory, southern Ohio, Indiana, and Illinois were relatively supportive of the Confederacy because they wee economically integrated with the slave economy of the southern states. Had trade from that region been more with Virginia than with New York and Pennsylvania, there may have been no President Lincoln - and perhaps no 13th, 14th, and 15th Amendments either...

