 Key mitochondrial proteins aren't necessarily in mtDNA

E.g. in humans the adenine nucleotide translocator is present in chromosome 4, not in mtDNA.

These have almost certainly been transferred to nuclear DNA in the course of evolution.

This isn't completely surprising, since when mitochondria die, their DNA is kind of left in the cell, so it is not hard to imagine how genes end up getting uptaken by the nucleus. This is suggested at Power, Sex, Suicide by Nick Lane (2006) page 196.

A limiting factor appears to be that you can't just past those genes in the nucleus, further mutations are necessary for mitochondrial protein import to work, apparenty some kind of tagging with extra amino acids.

However, you likely don't want to remove all genes from the mitochondria because mitochondria have DNA because they need to be controlled individually.