They don't deserve a thing just because they won their 4th rate leagues. They need to prove that they aren't just good when they're up against championship (or probably less) quality teams. Very often they don't, so they don't qualify .. obviously teams that finish top four in Europe's top leagues are better than whatever team won Denmark's top tier league.
Also, the majority ARE 'glory hunting armchair fans'. Most football fans aren't hardcore local match goers, not everybody treats the game as seriously as you do. Most people are perfectly content with the current format and are very happy just watching a CL game on the TV after work or at the pub, and they would have zero interest in watching APOEL vs Krakow or whatever. People want to watch elite talents in competitive fixtures.
The teams that drop out of the CL very often actually win the Europa League (Chelsea, Atletico, Sevilla) because surprise surprise, the CL is a hell of a lot harder than the 4 qualifiers you play to get in the EL.