One should distinguish between "rivers" and "navigable rivers". Some are too shallow for major traffic, some have rapids, and some simply don't lead to anything important. Others tie key cities and/or resources together, and become major transport routes. Canals were often used to turn less-navigable waterways into useful ones, or connect nearby waterways. Railroads gradually usurped a large share of the workload in many areas, rendering many or most canals economically non-viable, but moving bulk cargo by barge to coastal ports/cities is still an important function. By the end of the game, the importance of roads should begin to be felt, as truck traffic gradually becomes a "thing".
More than just small bonuses or penalties to productivity, there should be major adjustments in the construction costs and times and maintenance costs of infrastructure and certain buildings in regions where they're difficult to construct. Building a railroad across the Sahara Desert simply shouldn't be an option. Cutting a canal across the Isthmus of Panama should be all but impossible until the tools to do so are invented, and it will STILL be a massive and costly undertaking for even a major power. Building a railroad through/over a mountain range should be extremely expensive and slow, with reduced productivity due to its high maintenance costs. Still, if you NEED to move stuff across it, the higher costs may be well worth it.
The cost differences due to natural features had a huge impact on what was built where, and should do so in the game as well. It was no accident that most major cities developed along rivers or near a river mouth. It was also no accident that small towns along rail lines typically experienced rapid growth compared to those bypassed by the newly-built rail systems. Generally speaking, in-game effects should have a cause, not just happen randomly.
Agreed whole heartedly. In fact, just distinguishing between navigable and non-navigable rivers is the bare minimum. There are estuaries where ocean going ships can sail up (such as going up the Hudson all the way to Albany) and others that, while extremely navigable, can only accomodate barge traffic, like the Mississippi. Speaking of Albany, there's a reason why cities are often founded further inland along rivers, because that might be the limit for ocean going ships, or it might be at the fall line, where the river becomes generally non-navigable, etc. Then, as you've mentioned, there's rivers that, while generally non-navigable, can be canalized so as to become navigable. And this is, of course, well before considering the entire issue of canals themselves (which I know the Devs have said they have thoughts about).
Or how about the freezing and thawing of rivers? Another key factor. Especially, for example, in Russia and Siberia, where the north-flowing rivers thaw out from their sources down to their mouths, resulting in massive ice dams, rendering said rivers much less useful (actually, rendering them as major obstacles).
And yes, trains and trucks do have their place, with (at least in our current age) trains being the middle ground between canals and trucks in terms of flexibility and cost (a truck can go almost anywhere, but is the most expensive of the 3, a canal or river can only go along its given route, but is the cheapest, and rail is in between).
I don't want to derail this thread on the military aspects further, but this is something that I think could be a big step up for the next generation of Paradox games.