I think it's normal to have that reaction to Sondheim. It may be a Disney movie, but it's ultimately a Sondheim show, and it's a very Sondheim show regardless of how accessible it seems at first. In some way, that's part of the beauty of the show, the deceptive simplicity of it (and something that seems inherent to its themes). I doubt the first time I saw the show (and I saw it as a teenager much like many young people are discovering it now) I thought the music was brilliant--though "Last Midnight" and I fell in love at first sight, er, listen. I probably even dismissed it as "easier Sondheim" when I discovered Sondheim and was all into being a young intellectual. The older I get, the more I return to it though. The songs, which seemed cute and "easy" when I was younger, have such a different context in my life; the rhymes only get more fascinating the more I discover them (seriously, "we've no time to sit and dither while her withers wither with her" is one of the most genius things I've ever heard); and my understanding of the meaning of songs like "It Takes Two" and "No One Is Alone" has become more complex and I'm sure it'll continue to do so. Not that this will happen to everyone, but I'm sure that as some of the young people who just discovered the piece grow older and keep coming back to it, they'll start seeing how pointed, poignant, deep, incisive and clever the songs are.
"Some people can thrive and bloom living life in a living room, that's perfect for some people of one hundred and five. But I at least gotta try, when I think of all the sights that I gotta see, all the places I gotta play, all the things that I gotta be at"