I think it could just be that America is a much bigger market with much higher production values in TV and Film, so British people get their fill of competent, triumphant heroes from American media.

America has plenty of beloved sad sacks too. Charlie Brown, Donald Duck, Goofy, George Costanza, Eeyore (originally British but very popular in America and popularized by Disney) to name a few.

British media has carved out a bit of a niche for itself, but British people are also consuming other English language media.

And you also have plenty of British media where the hero is competent, triumphant, masterful, and autonomous with (frequent if not ubiquitous) standard happy endings. Lord of the Rings, Harry Potter, Sherlock Holmes, Doctor Who.