Anna:
Believe it or not, most Koreans don't listen to idol music. It's like in most countries, they know of the bigger more popular and longer in the market artists. And pop isn't for all unfortunately. I for one can testify that even my own mother doesn't even like the newer, yet popular, artists in our own country. She likes classical and blues which is not uncommon but even so she doesn't know the younger artists.
I agree with you that not all Koreans listen to idol music but it's clear that in Asia boy/girl groups are incredibly popular especially when compared to Western countries.
The #1 selling album of all time is a boy band. Out of the top 10 selling albums of all time - 1 is a solo act (IU). If you really want to quibble 1 of the other acts is 2 guys so maybe not quite a "group". If you want to focus solely on physical sales of all time which should mean older people will be represented better - the #1 album is still a boy band. The top 3 spots - 2 are boy bands, 1 is a solo artist. If we look at the top 10 - the majority is still boy & girl idol groups.
Lets compare to the US physical album sales of all time: The top 10 is rock bands and solo artists. Top 20? Same thing. Top 30? Same. Top 40? Still no idol groups. Top 50? Finally at #41 we get the Backstreet Boys. 1 in 50. If we look at the top selling album per year to shorten history - we have to go back to 2000 with NSync to have an idol group land top selling album. Backstreet Boys and Spice Girls each had a top selling album in the late 90s as well. If we look at sales within the last ~5-7 years, One Direction might crack the top 20 with one of its albums.
Ultimately I don't really listen to idol groups, maybe I'll give it a go one day but for now I have enough music that I enjoy so I haven't felt the urge to give it a chance.
As for singers - Asaf Avidan comes to mind. I like the sound of his voice especially in One Day.
If you're into a stronger, heavier rock the lead singer of Skindred has a really interesting and good voice (I don't want to say metal because then metal fans get upset and say 'no it's not metal').
Melody Gardot for a more classical jazz sound.
I just picked ones few have probably heard of because I'm sure in 19 pages the big names have all been mentioned.