Rivers, particularly wide rivers, have always been a problematic feature in civ. In civ 1 and 2, rivers gave a movement bonus, so units could move up and down rivers quickly in riverboats. This is very realistic for ancient, and middle age units, but not so realistic for industrial and modern units. So in civ 3 and 4, this effect was removed, and a new defensive bonus to rivers was added. But many historic events were made possible by the mobility rivers afforded. The only way to reproduce these effects in later civ was to make significant rivers into ocean tiles. But this has many problems, most notably of bridges.
Perhaps a solution is to give most units the special ability to travel to another tile along the same river. Maybe ad a restriction on passing by enemies, or when enemies hold both banks. The modern unit problem can be solved b not allowing most modern units to have this ability. Units such as Catapults would not use it either.