It used to be used to detect spina bifida and still is in some countries, but they now use a detailled anomaly scan because, in the case of a raised AFP blood test, there's a much higher risk of m/c with an amnio - I seem to remember them saying 10% rather than the usual 1%.
Plus all it would tell you is that there's a high AFP level in the amniotic fluid as well as in your bloodstream - not what's caused it, so it could be spina bifida (the more serios open types - the less serious types don't show up at all), or anencephaly, or a couple of conditions where the abdominal wall hasn't closed properly. They could check the AFP levels in the amnio sample if they were doing it anyway, but they'd be unlikely to advise an amnio to look for neural tube defects.
I had a raised AFP blood (triple) test and they then did lots of anomaly scans - I never had an amnio - they couldn't find anything wrong. With an anomaly scan they can tell you what the problem is, and there's obviously a big difference between a small abdominal wall defect that just needs fixing after birth (or as in our case an eye problem) and some of the other much more serious things that cause high AFP. With an amnio, all they can tell you is that it's high.
A raised AFP blood test result could be the result of any one of three things: the fetus is producing very large amount of AFP (dates wrong, twins, some anomalies etc), too much AFP is leaking out of the fetus into the amniotic fluid (anomalies including NTDs), or too much is going through the placenta into the mother's blood (placental problems). The latter problem wouldn't be picked up by an amnio so the blood test result is more useful as they can check all the possibilities - especially the risk of placental failure as the pregnancy progresses.
DS was born with an eye condition (cataracts) that probably caused the raised AFP. I'm very glad I didn't live in a country where I would have had an amnio for raised AFP as it could have led to me miscarrying DS.