What is good singing? Can anyone capture it in words?
All kinds of singing can be considered “good” for all kinds of reasons. Certainly, if one applies the thinking of the typical “classical” voice teacher to all styles, then some singing is “more good” than others. Clearly, I do not adhere to that at all in terms of style.
What I do think, though, is that singing has to have some kind of integrity unto itself and to the artist singing. If it doesn’t have that, it cannot be “good”. Integrity is defined in the Webster College Dictionary as being “fidelity to moral principles; honesty; or soundness; completeness”. To me, that means that if you don’t know what style you are singing and you don’t know the accepted parameters of that style either musically or vocally, and if you don’t know the boundaries of your own vocal production, you are singing without integrity, regardless of what style you are singing. That can never be “good”.
When the artist Pink sang at the Grammy award ceremonies in front of Liza Minelli, “Somewhere Over The Rainbow” she murdered the song. Having no clue about how to perform it nor how to sing it in anything other than a crude, sloppy manner, it was in very bad taste. I felt very sorry for Liza. I like Pink. I think she is an interesting artist. She just had no clue and someone should have told her so. Guess not.
When Deborah Voigt sang “Annie” in the Glimmerglass production of Annie Get Your Gun, there was no integrity in that performance. She sang “Annie” as Debbie, suiting her own vocal capabilities regardless of the way the character was written to be portrayed. Unfortunately, since the role was written for a belter and Debbie wasn’t about to belt, (since she (a) has very little chest register to begin with and (b) certainly doesn’t take what little she has up very far in pitch, and (c) was about to sing her first “Brunnhilde” at the Met a few months later), she turned the role of a  young woman who starts out as an backwoods hick into something unrecognizable. Too bad for Irving Berlin. He’s been dead a long time so why not stomp on his composition because if you are a Diva at the Met, who’s going to stop you?
Then, of course, there’s the highly commercially successful (as in it made a lot of money for the TV network) Sound of Music with Carrie Underwood. There we had a natural belter from Oklahoma unable to make herself into a European woman who was aspiring to be in the convent just before the second World War. Oh well, who cares if you don’t have a mezzo-soprano voice or acting skills when you can bring in 18 million viewers?
What constitutes good? Staying on pitch? Singing a style as if you know what the style is supposed to be? Understanding the limitations of your own vocal output? Truth be told, there are no voice police and whatever “standards” there may be are arbitrary, subjective, felicitous, and fleeting. Today’s “great” was yesterday’s “so-so”. Today’s “successful” was yesterday’s “crass”. This is not going to go the other way any time soon. Of course, that means today’s “so-so” might be tomorrow’s “wonderful”. We just don’t know.
Therefore, when you see and hear someone who is singing in any way that presents a cohesive whole, be appreciative. If the person and the performance and the music hang together uniquely but effortlessly, that’s about as “good” as it gets.