There are a lot of reasons why karaoke doesn't sound "great" for the English VA.
It's a song that was originally Japanese and changed to English. It's very tough to match the beat of a song with the lyrics, have the words sounds like they make sense, and still convey the meaning. You could have the best English singer in the world with the widest range and it just doesn't help if the song doesn't flow right in English.
Japanese actors tend to be "multi threat" in their talents. There are a ton of great singers among Japanese actors, whereas that's not so common with Western actors.
The songs were written for the Japanese VA in mind to sing. Kaiji Tang might be a decent singer for all we know, but "The Future I Dreamed Of" may be further out of his register. It's rather high-pitched in the chorus and he seems to be more comfortable in baritone registers.
Greg Chun absolutely nails Baka Mitai. So that's not really a #4, but I have to say that.
I'm not saying it's a bad thing that the characters don't sound great at karaoke. In fact it actually fits more inline with the theme of them being a party and of them relying on each other to succeed rather than succeeding on one's own, which is more Kiryu's style.