I'm not really a sinew guy, but I don't think there is much WRONG with a smooth single layer on a square cross section, it just isn't necessary. Same benefit with a crown of sinew, less sinew (and sinew is heavier than wood), and you don't NEED the sinew at the sides to protect the wood on the sides because the neutral plane has been moved enough to protect both the back and belly side of the wood from strain.
I don't know about that allowing a longer draw on a narrower bow or not. Not sure I understand the question. The enemy to defeat on a narrow bow is belly strain, usually, which can be countered by added length, and well made longer bows with an intact growth ring, etc. then don't need the sinew. A sinew backing WOULD allow a longer draw on a shorter bow by preventing breakage. But, a narrow bow means a thicker bow, generally, and while sinew would protect the belly, too, I think less so as the bow becomes thicker. The sinew can only stretch so far, and the thicker, narrow bow moves the neutral plane again.
Think about horn bows, which can be pretty narrow, because horn is more compression elastic than wood, and the sinew and horn work together. Then think of an arctic bow with a cable backing. Most of those are fairly thin and have a raised or bridged cable, making them essentially thicker front to back. Does filling the middle in between cable and wood with more wood and making them longer gain you much? I don't know.