"God Only Knows" is pretty much the best pop song ever written, at least by my standards. As such, trying to cover it only reinforces the greatness of the original, while potentially exposing the covering artist's flaws. But sure Rivers; take a stab at it.
The Weezer frontman's solo piano take is much more personal than the Beach Boys' version but only as affective as a cover by any mildly talented singer would be. It's unclear why Rivers Cuomo decided to record himself playing this song, and it's certainly a nice moment to watch, but no one's ever going to beg to hear the Rivers Cuomo version of "God Only Knows."
Really, this just proves that "God Only Knows" is still a great song. Not like anyone forgot.