Lawrence Gough’s description to Den of Geek of the deleted scene indicates that it would have made for a wonderful addition to the story, but the episode didn’t really suffer for it being cut out.
While the purpose of the premiere was really to build a bond between the Doctor and Bill to justify the decision to travel through time and space together, the heart of the episode came from the developing relationship between Bill and her crush, Heather.
When the two met and began to crush on each other, they kicked off a sequence of events that would sadly see the end of Heather but introduce Bill to a world larger than what she knew before.