There's no issue with asking and it is helpful for doctors to know. The reality is some Mums would refuse a breath or blood test, regularly miss appointments and misreport. I'm not against being asked about it, but I don't see how it helps in a number of cases as information would be unreliable and so actually may put GPs and Paeds off the the diagnosis if not included in the notes. FASD can be hard to diagnose, many more children than diagnosed will have FASD but present with autism, ADHD etc. Mums can sometimes be unaware of a pregnancy, as a PP mentioned, or not realise that a single glass of wine can cause issues. It's always been advertised that very light drinking during pregnancy is acceptable (a glass of wine) and an easier cut off can be just no alcohol at all. Recently, with new information about FASD and FAS, there is now guidance that no alcohol through pregnancy is safe. Again, with studies and self-reporting, it can be hard to pinpoint if one glass is or isn't an issue and why it effects some neonates much more than others. Many women also seem unaware of what a small glass of wine or measure of spirit is.
In the same way in adoption, Mums sometimes say they haven't drunk and there will be no record of them 'presenting intoxicated' to professionals during the pregnancy, but sometimes the child is found to have FASD or a related condition much later on (6+). Not all by any means, but some. It won't actually help hugely in adoption due to the unreliability of information and the fact if a women turns up with no alcohol in her system, they cannot guarantee she will not go home and drink that night. I do have empathy for women struggling with addiction issues through pregnancy, some of these women are in (and have been through) terrible situations and are not able to put their child first. It's horrendously sad for the child, but it's sad for the mother too.
I think raising awareness is the best way. Educate all women (and men too) about FASD, FAS and alcohol in pregnancy. Educate around amount of alcohol during pregnancy (ideally none), the risks of drinking (related foetal alcohol spectrum disorders and the mental, emotional and physical risks this poses eg. memory problems, inability to understand consequence, vision problems etc.), show women what a baby withdrawing from alcohol looks like (there are dolls used as aids) etc. Give women knowledge and support they can access if they want to stop drinking and are struggling. Give GPs a good awareness around recognising possible FASD and FAS (can be hit and miss). Not only this, but help teachers to understand it too. That would help in adoptive families - if more schools understood foetal alcohol related conditions and what they meant! Support needs to be wider reaching, as does diagnosis (there is only one centre for complicated diagnosis, I believe, in the UK). A lot of children with foetal alcohol issues are complicated to diagnose, they do not present with facial features and may be within milestones. There needs to be much more education and support around the whole issue.