The British did try for a more southern border, but it elicited such negative reaction (including a demand that US territory extend all the way north to Russian Alaska) that there was little choice but to drop the issue.
To the Americans of the era, any British land south of the 49th would be regarded as having been somehow stolen. They would look at a map and see the nice straight line of the 49th give way to a jagged intrusion of British territory - and contrast that with the similarly nice straight line then defining the border with Mexico. Even if the Americans had been in the least bit inclined to agree to a border along the Columbia, they could have argued fairly persuasively that that border should continue upstream along the Kootenay River to the 49th (see
map).
As it was, the Americans had already tried in 1818 to get the 49th extended all the way to the Pacific as the border. And therein lies the actual problem and where and when the blame should be placed: the British should never have agreed to a boundary across the prairies based on a line of latitude in the first place. Once they did that, it was virtually inevitable that the border across the mountains would continue along that line.