Our healthboard also has this policy. I only had 12 week scans for both my pregnancies (until I was overdue with both of them and had scans at 41 weeks). I probably would have preferred to have had a twenty week scan but I also think it is gives false reassurance. Yes it can show some anomalies but it is no guarantee your baby will be born in perfect health. It can also give false indications of problems which can cause a lot of unnecessary worry.
I think your midwife has a point. Yes it would be good to know if your baby has any abnormalities, but the 20 week scan doesn't tell you that for certain. And in a cash strapped health authority where only one automatic scan is given, the dating one is more important. You will get as many scans as you need should you have any problems.
Good luck with your pregnancy! Relax and try not to think about what problems there might be. I know it's easier to say!