"Here I Come" was not cut pre-Broadway, as I saw it performed during early Broadway previews when the show was still two acts. It was during previews that the intermission was removed and "Here I Come" and "Opportunity" were scrapped along with it.
"Here I Come" suffered from very poor staging, even though I like listening to the song on the recording. As I remember it, Evan had just been exposed as a fraud during the viewing of The Blood Master and he ran out of the movie theater and into the arcade. The whole school, including his two genuine friends, had turned against him and he's all alone. He started singing "Here I Come" where he was joined by the entire school who had just turned their backs on him! It made no sense. Why would all the kids who had just shunned him all of a sudden start singing about how he's going to make a comeback?
On top of that, the choreography was a Dance Dance Revolution thing that was just silly.
Marie: Don't be in such a hurry about that pretty little chippy in Frisco.
Tony: Eh, she's a no chip!