Well, how would those two answers explain why it is still extremely popular? No, I don't think they's the reasons.
First of all, as cheesy as the story is - it's still a good story. It sucks you in, and you're rooting for the main characters.
Secondly, it's fluffy fun but also deals with issues that people relate to, like the mother-daughter relationship, a broken heart etc.
Also, you're forgetting the mass tourist appeal; ABBA may not have been that popular in the states, but they were HUGE all over Europe, the Middle East and Australia, and they are still well-loved. Their songs are part of people's lives (for example, I remember dancing to "Money Money Money" at age 6!)and they have great nostalgia for them.
Add to that the talented performers, the world wide reputation and the glitzy costumes...and you've got a hit!
"Years from now, when you talk about this - And you will - Be kind. "