Is it just for theatrics that in Nerve, no one ever even considers pressing the "reject" option on their phone during the game?
Yes. Without it there would be no movie. The movie revolves around going big or going home. Adventurous young adults with no impulse control.
I thought they made it clear that you could reject, or bail, but if you do so, you are out of the running for the top prize.
Sydney bails, after all: from here:
Jealous at Vee's rise of popularity, Sydney accepts a dare to walk across a ladder suspended between two buildings. Whilst performing the dare, she drops her phone and becomes scared. Sydney bails out and loses the game. Ian takes Vee to Sydney's party and Vee catches her in bed with J.P. After arguing with Sydney, Vee receives and completes the dare on which Sydney bailed.