Sending White to the bench would be both good and bad
As for White coming off the bench, he has experience playing in the second unit and his playmaking would definitely be an asset. Also, while his scoring has definitely been a disappointment, it would be consistent with an above-average bench player.
Of course, there are some downsides too, which keep breaking up the Murray-White pairing from being a no-brainer. For instance, moving White to the bench is unlikely to serve as the confidence booster that he needs.
The last thing San Antonio needs is for him to play worse. Benching White could also lead to questions about his contract, overall value, and even his future with the team. After all, he's making an average of $17.5 million per year and has been outplayed by a second-year player. Additionally, he’s the oldest of San Antonio's young players and appears to be the most likely to be eventually moved, especially with his play this season.
Ultimately, the decision to continue to start Murray and White together is a complicated one. Hopefully, White's play can improve enough to warrant him continuing to start. Were that the case, then he'd definitely provide a useful backcourt mate to Murray. One who can knock down open shots, score and pass out of the pick and roll, and defend.
On the other hand, if he continues to play as he has, it's hard to justify not starting Vassell over him. With the Spurs entering a particularly difficult stretch, White could still snap out of his funk and help keep the team from going into a tailspin.
However, if he can't then the Spurs could bench him, though it could further affect his poor play and unintentionally sabotage the bench by pairing him with another disappointment, Lonnie Walker. The decision to continue to start White and Murray is a double-edged sword, but it may need to change without some positive trends coming very soon.