You are correct to say 02 and H2 are boiled out. But when referring to distillation that is not the point. My misunderstanding.
When distilling, contaminants are not boiled out. Water is boiled however, but the point is to recollect the water vapor. Recollecting the vapor and allowing it to condense will give you pure water. That is why it tastes flatter than the reverse osmosis unit. The RO is not as pure.
Yeah I'm familiar with RO systems. Most labs use a similar system when they need to use lab grade water. However, it is a lot bigger with many more levels of filters.