I have no problem with dissonance. I enjoy composers such as
Schoenberg or
Messiaen who use creative and adventurous sonorities to create bewitching sound worlds. But if you strip away the poor performance from the Denpa OP, it's just a standard pop song. It's rhythmically stagnant, harmonically restricted to a few basic triadic progressions, and melodically built around repetitive motives. Musically the only interesting part is the contrast between the heavy and dark instrumental accompaniment and the very high and hollow solo vocalist.
I'm not sure what you're talking about with the vocal style, since it sounds pretty non-legato to me. What bothers me most about the soloist's singing is how physically unhealthy it is. There's no breath support; she's just forcing the sound straight through a tense throat and pinched nose. She's going to exhaust her voice trying to keep that up, so hopefully it's not how she sings all the time.
I'm sure everything is intentional and that this song fits its lyrics and Denpa Onna very well. But out of context, it's just a bad song.