It didn't work for me for one simple reason.
The big problem with the story is that there is too little consequence to losing the trial for Niven's character. The afterlife he would be subjected to if he loses his case seems benign, pleasant, in some ways preferable to "life".
If he loses, a quick and painless transition to "death", followed by an eternity of no more worries, no stress, no aging, and the company of lost friends and relatives. Plus the ability to hobnob with the greats of human history. There seems to be no downside. If the carnal pleasures are denied in this "heaven", then the movie didn't adequately explain that. (I suppose one could possibly infer this from the lack of Technicolor in the heaven scenes, but wouldn't that make this afterlife hell rather than heaven?) This, weighed against being able to screw around for a few decades with a WAC sergeant he talked to for 5 minutes over the radio if he wins.
Similar stories at least have the threat of an eternity in HELL as the booby prize, with a reprieve granted as an opportunity to redeem oneself from this fate. That kind of raises the stakes. In "Stairway to Heaven" I couldn't have cared less about Niven's character winning or losing his case. It's basically a "If you win, 5 cookies - if you lose, only 4 cookies for you" situation. Either way, you still get tasty cookies.