I was reading about the lake Constance and it seems the river might actually somehow be flowing through the lakes as the river water doesn’t completely blend with the water of the lake, at least this is what WP hinted at in one article. On the other hand, looking at the names is somehow revealing.
For non-German speakers, for the following paragraph you only have to know that “See” in German means lake. Now to the names: there is the “Alpenrhein”, which commonly is seen ending at its inflow in the lake (Obersee), then there is the “Seerhein”, which is actually just the 4km of connection between the Obersee and Untersee, and leaving the lake, there is the Hochrhein, but between the Alpenrhein and the Seerhein there is the “Obersee” for about 30-40km and no indication of any river in the name, while between the Hochrhein and the Seerhein in the Untersee, part of it is called the “Rheinsee”, what a nice mix of river and lake, although the classification indicates “lake”.
While there clearly is continuity in the river names (all Rhein), the parts in the bigger lake are just named as lake, because this is what you perceive.
I am not opposing the idea to have continuity between inflows and outflows, but these should not be tagged as waterway=river or at least have an additional tag like river=lake (oxymoron?) where there isn’t any river (flow). I could imagine this continuity requirement already be satisfied by connecting the inflows and outflows to the lake outline, but I would also be ok with explicit connections if they are deemed advantegous.