It's not in my top 100 or 150 or 200 top favorite movies of all time. I can see why it's a beloved movie.
It's all a matter of perspective (generationally speaking). A lot of people first saw it in their teens or twenties. So, there's the sentimentality factor you're glossing over.
As a film deconstructed and looked at piece by piece? All parts hit their mark and do so consistently. Great acting. Snappy dialogue. Characters the viewer can relate to or at least end up caring about. Emotionally tugworthy score. Key plot points timed perfectly to grab the viewer and tug at his or her heartstrings. Also, it's a product of the 1990's.
They couldn't make this movie in the 1970's. The Shawshank Redemption protagonist is too smart. He's definitely likable. Protagonists of the 1970's are dumb antiheros who couldn't cross the street to save their respective lives, (eg. Babe from Marathon Man (1976) for example).
The villains are iconic (though a tad 1 dimensional). When it comes to populist films, don't discount happy endings.