I've said before but Love Live is less an idol show and more a character drama about a club who happen to do idol related activities.
People like it because of the characters and their chemistry with each other. In terms of story most of the songs are completely nonsensical, very muscialesque in that they are part of their own universe separate from the actions of the real world. You only have to watch the first episode for an example of that and, since it was mentioned, the movie is an even greater example. Compare this to other idol shows where every performance is on a stage of some kind, yes, even AKB0048 with all it's crazy shenanigans follows this rule.
If anything the idol aspect results in some very silly aspects; like the cast discovering merchandise of themselves raising the question of where the photos for that merch came from, Maki and Umi managing to write a discography in one year that shames most professionals, why are there subunit singles when the show never mentions subunits once etc. (obviously the last one is because Love Live started as a fictional group which got the anime later, no need to inform me of that)
People compare it to The iDOLM@STER a lot but honestly you're better off comparing it to K-On.