Home distillation probably only works if you have all copper plumbing instead of the PVC or PEX plumbing that a lot of homes have. But copper plumbing is probanly going to leach various metals into the water.
Some volatiles are going to come through (which can be mostly mitigated with an activated charcoal filter at some point in the process), but you’re vaporizing the water and condensing it back into a liquid, leaving behind stuff like metal and microplastics.