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2/4/6/8x
Before that, with true doubling, they were absolutely broken.
If they only gave +1x per additional river, as you mentioned, there would be hardly any reason to run rivers as you'd get the same benefit by just placing that tile down instead.
The way it currently works is a compromise to keep the tile from being broken, while also retaining its usefulness & making it require some thought on how to place.
It is understandable that true doubling would be way too strong. But in my opinion, there would still be enough of a reason to take it in your deck if it only gave + 1x per additional river. It basically would increase your chances to get the effect of landscape tiles. Assuming every card is evenly likely to drop and you have 10 cards of which one is a landscape tile you want to get as many of as possible you would have a chance of 10% it drops. If you add the river card you would increase your chances from 1 out of 10 to 2 out of 11 which would be around 18%. So you would nearly double your chances.
roadside/path/special cards are weight 2-4 (except wheat field is 6)
Rock/Mountain & Forest/Thick are 12+10
Desert/Dune is 10+8
Suburb is 18
Meadow is 15
River is 14
You generally want less, not more.
Once you have bridge river can be a landscape that also make lots of mob spawners if you really want.
Rivers are better than just straight land though - lets say you do simple full columns:
thicket + river = 4% = 2%/tile, okay...
thicket + river + thicket = 8% = 2.67%/tile (river+thicket+river is the same)
thicket + river + thicket + river = 12% = 3%/tile (again, same if you start with river)
thicket + river + thicket + river + thicket = 16% = 3.2%/tile (also same if you start with river)