in the end it'll still be 'disk like'. You build along the river, distances are getting big and suddenly you realize there's a lot of unused space where you can expand the building of the city while maintaining short commute time(building perpendicular to the river/expanding the width of the city), meaning even more money, more people, more economic activity. In fact most of big cities built on rivers started as small communes that gradually expanded in each direction

Countless major cities and towns are built on either side a river. Anything beyond a village quickly evolves in to something roughly circular.