I would say: It depends.
The Lake of Constance (Bodensee), which has already been mentioned earlier, is Germany’s largest inland waterbody and was largely formed by erosion in the Jurassic period. The river Rhine was deepened by pushing off the Rhine glacier, which finally formed a lake. Historically, the Rhine River existed first, and Lake Constance then formed around the river. (Very basic explanation)
It would be wrong, at least from my point of view, to interrupt the river and all connections at this point.
My personal argument for connecting rivers and streams through lakes and reservoirs is that if I throw a small paper boat in at any spring in the Rhine catchment area, that paper boat (or microplastic) will sooner or later end up in the North Sea.