The Roger Federer-inspired Swiss stunned Williams in round one, but was no match for the Thai star who moved into a Grand Slam third round for the first time.
Bencic, 20, was never in contention on a searing day on Hisense Arena, slumping 6-1 in the first set before putting up more fight in the second only to succumb 6-3.
Bencic, who made her WTA Tour debut as a 14-year-old, has often been touted as a future potential champion, but she again failed to live up to the hype.
"She's still so young, she has a great career ahead of herself. I try to help her where I can," he said.
But he also added: "Still so much to improve."
For Kumkhum, it was a major achievement in her seventh Grand Slam main draw appearance.
She lists her best tennis memory as reaching the second round at Melbourne Park in 2013, which she must now surely revise.
"This is the best win of my career," she said afterwards.
"I kept telling my coach and family that I want to pass the second round, so I'm really happy.
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