My missile tech sucks, and so do my missile researchers. I'm going to tech up in this area a lot quite soon. I havn't put up missile PDC, and am considering beam PDC as earth defense, stationed on Luna.
Good idea? Bad idea? Meh idea?
That's a decent enough idea if your tech is high enough. The moon is around 380,000 km away from the Earth. The beam warship in the tutorial (relatively early technology) only has a range of 180,000 km, so it wouldn't be able to cover Earth from all (or even most) angles. Once you got a range of 600,000 km or so then you would always be able to cover the Earth. One half of it would be significantly more exposed than the other half, but against the AI that's not likely to be too much of an issue, and the fluff value may be worth it. (As well as the cost benefits from PDCs).
What I would do instead is make large orbital defense stations. No engines, minimal maintenance, good armor and a lot of weapons. When a combat ship is in orbit around a colony it doesn't deteriorate (as long as there are enough Maintenance facilities for a ship of its size) so that's not an issue, and it's out of the atmosphere so beam weapons aren't hurt. It's not quite as cheap as a PDC, but the lack of engines helps a lot.
The best part is that you can move them around via tug when circumstances change. Pay attention to their expected lifetime when you do this though. If you penny-pinched enough it should be abysmal, so with a slow tug there is a danger of it breaking down before it reaches its destination. Make sure that you design a tug with enough extra maintenance that it can continuously restock the defense station during its journey.