What extending the existing parallel border across (excluding Vancouver Island) does is that it creates a nice "scientific" border that never changes course (such as a river may), and is easier to to "prove" than using a drainage basin (original border) or continental divide. The HBC for the most part south of that line didn't care too much about whose laws were in effect during the condominium (mostly American law was enforced btw) as long as their fur trading rights were protected; which after buying out John Jacob Astor they were.
Without extending that border there are two options- all goes to Britain (no, won't happen after decades of 54-40 or fight and the sizable American population south of Columbia and Snake) or more likely- columbia and snake rivers and Continental Divide become the border to the existing latitude of America and "Canada" since 1818 when the US last gave up any territory (2 minor river valleys in return for the southern half of the Metis inhabited Red River Colony). Both seem less "easy" than just extending an existing border latitude. Rivers can shift location before any systematic mapping, and disputes of "the river was over THERE when the treaty went into effect" not to mention rivers cause conflict over riparian use, irrigation and damming rights, commerce and shipping, rivers make horrible boundaries (eg-the US and Mexico have had several land swaps in the second half of the 20th century along the Rio, including the Country Club dispute), then there's the problem of the Continental Divide and marking it.
The reason the British came to the conclusion they did when they did was BECAUSE of the Mexican-American War. There's no PoD being mentioned that would make the British suddenly say- "the Americans just mobilized a good sized army and executed a fairly descent campaign using a navy and blockade, occupied Mexico City and could do anything with Mexico they want. They could turn and use it on Canada, let's give them Oregon". The fact is that in 1848 Oregon is going American, as long as there's a Mexican American War.