Stanley is the only logical choice to commit this act of ultimate revelation. He alone refuses to buy into Blanche's ruse of youth and beauty, manners and sophistication.
However, in order to fully understand the importance of his act, one must consider the lantern in earlier scenes. In Scene 3, Blanche insists that Mitch, one of Stanley's poker buddies, cover up the harsh light from the bedroom's unshaded bulb. Blanche has marked Mitch for her next beau, and fears that the light will reveal her age and flaws. Mitch, her willing victim, is more than ready to accept her explanation: "I can't stand a naked light bulb, any more than I can a rude remark or a vulgar action." It makes him feel like he is "special" enough for Blanche.
By Scene 10, the lantern is a crucial component of the rape scene. Stanley growls: "I've been on to you from the start! Not once did you pull any wool over this boy's eyes! You come in here...and cover the light bulb with a paper lantern and lo and behold...you are the Queen of the Nile!"
When Blanche, broken and revealed, finally leaves, Stanley has no pity. When Blanche makes an attempt to come back into the apartment, he bellows: "You've left nothing here but spilt talcum...unless it's the paper lantern you want." He rips it off the bulb and Blanche "cries out as if the lantern was herself."
Stanley is the best character to tear the paper lantern from the bulb because he has the hottest temper. He is animalistic and acts instinctively throughout the play without first thinking of the repercussions of his actions. Anything done with brute force in the play is done by Stanley Kowalski and it's done without remorse, in fact he can find reasons to justify most of his barbaric actions, even the rape of Blanche. He tells her that she likes it and acts as though he's done her a service.