in my opinion, I wish we knew less about them. I feel that as singers, they are doing an art just like a painter or sculptor. i feel as if the music should just be a showcase (similar to a gallery), where we don't know as much about the artist but we know that they made the art and we know they have a personal meaning for the art.
i see how this can be a problem currently in kpop, where most artists do not create their own music (mostly... depends on the idol though.) but have a team creating the music for them and they just sing/perform the music.
now, i do realize that is the whole point of kpop is to "feel like you know your idol", but to a certain point, it feels like intrusion. like why should i know your blood type and your brother's name and your personal life details? i enjoy not knowing all the ins and outs about an idols life.