Like many others, I’m broadly in favour of mapping rivers through waterbodies, if it “seems like they flow through it”.
Things like the Bristol Channel, or St. Lawrence Estuary are coastlines, not lakes, so I wouldn’t put a river through them.
I don’t know about the local geography, but do people think Lake Victoria, or the Great Lakes are “lakes that are on rivers” or “lakes that are just there”? For some larger lakes, it makes sense to map through the lake, such as the lakes along the river Shannon in Ireland, or probably the Zambezi through Lake Kariba. (I will admit to having connected a few rivers throught that one).
We already map linear waterways through a natural=water (when people map the river area). So it sorta makes sense then for a river to go through a lake.
A waterway=river turning into a =canal is very common.
Ahhh! 
I don’t like when people map a river (waterway=river) through a lake, but without the name. e.g. the Rhine through Lake Constance. It was discussed on the forum #1, #2, #23. If you map waterway=river then you’re saying there is a river there. OK, so does this river have a name? Yes, it’s the Rhine. So why not put a name tag there? It sounds like just mapping for the renderer
[quote=“Minh Nguyễn, post:27, topic:104438”]
a renderer could layer the reservoir over the waterway or perform a spatial query to knock it out. Perhaps the possibility of a spatial query means we don’t need a new tag for the submerged portion of the river?[/quote]
I have no strong opinion on waterway=river or =lake for the way through a lake. I don’t think you’ll ever get OSM carto to change. 
I’m currently working on repairing the river basins map update process. Maybe I can add something that looks at natural=water.