Not to negate the halachic-mechanics answer (which I like), but I think there's psychology at play here as well. At a simpler level, all rights in Judaism are tied to obligations, and it's just not fair to leave people hanging. Here's this widow, trying to figure out what to do with her life now. It's either going to be "the brother will step up and do the right thing", or "he's not, so spit at him, then make a clean break and walk away from that family and start a new chapter." The brother needs to make a serious, one-time-and-this-is-final decision.
Recall that if the living brother does marry the widow, he becomes the heir to the deceased's estate as well. So suppose the living brother isn't super-mature or considerate. Right now he looks at his sister-in-law and thinks, "Hm ... I'm hot stuff, she's a Size 2, I bet I can find a Size 0 lady out there ...", so he does chalitza and drives off into the sunset in his flashy sports car.
Then, a few years later, he needs to pay for Botox, a hair transplant, and alimony from that Size 0 relationship that didn't work out (or worse, he's still married to Size 0 lady and wants an extra wife to bring in more money) -- and suddenly his dead brother's bank account looks quite attractive! So he calls up his brother's widow. "Hey, Shprintza ... remember me? Oh you're still single? That's fantasti!--umm, so sorry to hear that ... but you know ... we really ought to do the right thing for the memory of my dear brother and your dear husband, God rest his soul..."