You have to close your mouth for most consonants. I do believe that in some styles, the consonants ARE held. I can recall hearing someone finishing up a line with lovely ornamentation on an "N." The problem is that all the air then comes out your nose. Some styles are supposed to sound nasal and some aren't.

When you sing vowels, the air keeps flowing completely unimpeded. You can control the volume and even the - I don't know if there's a word for it - character of the note. Try singing an E and try moving things around - you can smile, open your mouth more, smile, close your mouth a bit so more of the air/sound comes out your nose, open your throat more. You don't have that control with a consonant.