I'm getting the science equivalent of nails down a chalk-board every time I hear/read the "three parent babies". Even "three person" winds me up a little bit but at least it isn't quite as emotive. I can see why the media has gone with that option as it is attention-grabbing and sort of works as a summary.
The problem is that I think it conjures up the wrong picture of it being an evenly split contribution from the three individuals and it's bait for conservative types who worry that the "traditional family unit will be destroyed" along with the laziest negative argument ever of "it isn't natural". I'll throw in my "I'm not a mitochondrial geneticist expert" disclaimer but mitochondrial DNA is a separate entity from our genomic DNA (it was probably a different organism billions of years ago), so while the DNA from Sperm and egg are shared 50:50 the mitochondrial DNA always (but not always because - nature isn't as conservative as some want to believe) comes from your mother. By the logic being applied in news headlines this means that the father is always the weaker contributor, genetically speaking. Maybe I'm not giving mitochondria it's due but I don't see them as that much different from the human microbiome (the huge number of micro-organisms that exist in our bodies). They are also largely inherited from your mother (pick them up during birth, from breast feeding and skin contact) but can also maybe pick them up from other people early in life. So you could have lots of "parents".
As for whether the technology should be used, I think a really important thing to remember is that most people aren't going to go for this type of fertility treatment unless they have a strong medical reason for doing so. It's not like Jessica Ennis is donating her mitochondria - although maybe that would make the UK more energetic? I can imagine the worst thing that could happen from this procedure is that it will screw up Mitochondrial lineage studies as the mitochondria may have come from a different person than the genomic mother.