I will attempt at rephrasing your interesting question after these considerations:
At the continental scale, flowing water has no significant inertia, so water flows following the maximum slope. A river is just a path along the continent that follows the maximum local slope at any of the places it passes through.
What amazes you (let me interpret) is that continents are mostly drained by rivers that flow continuously downslope. When water lacks a downslope path ahead (local topographic minimum), it forms a lake. So, the striking thing is that there are relatively few such topographic minima, lakes or marshes, in our continents.
If the river ends in the ocean, the fact that it is long is just imposed by the size of the continent and its sinuosity. If it ends in an endorheic (closed, internally-drained, intracontinental) basin, then by definition the river will form a lake at the lowest spot of the basin.
Because continents are above the level of the surrounding ocean, it is clear that between any location at the continent and the coast, every path will be, on average, downslope. Continental areas below sea level are by definition endorheic (see 3) and therefore they drain to internally-drained lakes.
Provided some slope, erosion makes the river network gradually entrench the terrain at typical rates of 0.01 to 1 mm/yr. Rivers move laterally more easily at very flat regions, where they loose energy and deposit their sediment load, forming meanders and marshes. Over geological time, the river network, together with other surface transport processes, make the landscape decay towards a flat (peneplain) surface at the level of the ocean.
So what would be the opposite to a landscape dominated by long rivers? Answer: Having many locations with no downhill slope to follow, topographic minima (basins) where lakes form.
Therefore your question reduces to this one:
"Why aren't there more lakes?"
The 117 million lakes on Earth occupy only 4% of the land surface. The rest of the continental surface has a downhill slope for water to flow. Even endorheic drainage basins are drained mostly by rivers, although these drain to close lakes instead of the ocean.
Importantly, large lakes are relatively rare because they are ephemeral: once they form by tectonic and geodynamic changes of the topography they tend to disappear due to two processes:
A) Lake basins tend to fill up with the sediment carried by tributary rivers.
B) Lake basins tend to be lowered in level due to the erosion along their outlet river, see my point #5 above.
Consider a landscape formed with a purely random topography. It will contain many lakes because their steepest descent path will not lead to the sea. Processes A and B would tend to fill the lakes and erode their outlets, making this topographic minima disappear and establishing a normal fluvial network with progressively fewer lakes.
On Earth, erosion is a process trying to remove lake basins in timescales of hundreds of thousands to tens of millions of years, depending on the size or elevation of the lake and its drainage basin. If we still have this 4% of the planet surface occupied by lakes it is because river erosion competes with relief-generating mechanisms such as plate tectonics or glaciers. But that's a different story.
: National Geographic: 117 Milion lakes in the planet.
: Carroll, A.R., and Bohacs, K.M., 1999, Stratigraphic classification of ancient lakes: Balancing tectonic and climatic controls: Geology, v. 27, p. 99–102, doi:10.1130/0091-7613(1999)027<0099:SCOALB>2.3.CO;2.
: Garcia-Castellanos, D., 2006. Long-term evolution of tectonic lakes: Climatic controls on the development of internally drained basins. In: Tectonics, Climate, and Landscape evolution. Eds.: S.D. Willett, N. Hovius, M.T. Brandon & D.M. Fisher. GSA Special Paper 398. 283-294. doi:10.1130/2006.2398(17)