I just want to point out - no judgement, a lot of people have very different feelings on this and it's all ok - but Down's is NOT the only chromosomal anomaly out there that's picked up by blood screening and amnio. Personally I would not terminate for Down's - it isn't associated with a super-high risk for other health problems (although Down's people usually have shorter life spans and are prone to cardiac issues later in life) nor is it associated with a lot of pain, suffering and surgery to make life even possible. Plenty of people with Down's live full, satisfying and happy lives.
But trisomy 13 and trisomy 18 are a whole different ball game. Very poor outcomes there, not much hope of a pain-free life, never mind full and happy adulthood. This is why I had blood testing done. I would be perfectly happy with a Down's baby. But I would not ask a baby to live with other trisomies, no matter how much I wanted that baby.
So I think that the BLOOD tests are a good idea - no risk to the fetus, and can provide peace of mind to the parents if they're negative (as most are). Amnio if the blood tests are negative isn't necessary as it's unlikely to show anything other than "all good" and it DOES carry some risk. The difficult choice, to my mind, is what steps do you take if the blood tests are positive. For me, it would become a statistical problem - risk of carrying a baby with a most-likely-fatal trisomy vs risk to a Down's baby vs risk to a potentially normal baby.
I don't think it's a good idea to avoid the blood tests simply because one is afraid of having to make decisions with the information they might provide. But, that's me. I understand that other people would prefer to defer those decisions to a higher power. I just think everyone needs to be very clear - to themselves - where they stand on that.