So the thought that Eskimos used sinew cable backs is erroneous?
Well, some bows undoubtedly used sinew and were much smaller without the massive cable. They are also likely to have been made of antler. Only baleen could ever provide that massive cable.
Why is that? Aren't ropes just made by adding more of the same?
Yes but you can only get so much sinew from a caribou. Think about how little sinew you get from four leg tendons and a backstrap, and compare that to what you get from baleen. Now consider that sinew had to be used for other, more pertinent tasks like sewing clothing and kayaks. There simply was not enough of this precious material to go around, particlarly among those further inshore.
An animal has tendons in the front of the legs too.
However I think sinew is a bit more readily stockpiled than hunting or finding whales for baleen. Speaking of precious material...
Maybe you should consider that the main part of the bow would be baleen?