if you check out the research forum you can find plenty of articles that will show that the brain can function just fine on ketones and I have even read somewhere that it can fucntion up to 25% better on ketones.

You get enough glucose in your 20g a day for any parts of your body that would need it and worst case assuming you didnt, your body can manufacture glucose through a process called gluconeogenesis.

If anything I would think the refeeds are more harmful. If you want to burn fat then you want your body to use ketones for energy and keep fat utilization by the body maximized.