My consultant was brilliant (I was 42). He had a decent and nuanced understanding of statistics, and realised that the statistical mean is not the whole story - the shape of the distribution, where you as an individual are on it, and why matter too (in my first meeting with me, he said "how do I, as a doctor, weigh up the relative risks of a healthy weight, non-smoking woman in her 40s who exercises regularly versus a woman in her twenties who smokes, drinks and is overweight?"). He explained carefully about the changes in statistical distribution for placental failure with maternal age...
Then things got more complicated - scans showed DS was small for dates. (Again, the "why" came in there - he said "There's an outside chance there's a problem with IUGR - but, given that you're small, I think genetics is a more likely explanation" - hence why I mentioned the "why" of where an individual is on the distribution). So then it became a question of two competing needs - the longer we could leave him "in" the bigger he'd be, but the higher the risk of placental failure. In the end the consultant let me go to 41 weeks, with doppler scans of cord blood flow and monitoring of amniotic fluid every couple of days (the placenta apparently tends not to fail abruptly, so providing you spot the start of things going wrong, you have a window of two or three days in which to deliver). He also opted for a CS on the grounds that he didn't want to put a small baby through the stress of an induction (he was happy about a VB if I went into labour naturally, but 41 weeks and the booked slot for the theatre time rolled round with DS only about 2/5 engaged and my cervix too closed to even attempt a sweep).
CS was very good in the end - a calm and lovely way of meeting DS and I was lucky in that the healing process was very good.
So, message to NHS - clone my consultant so there's several of him in every maternity unity in the country. Also clone my community midwife who said at the booking visit "consultants vary - some are sensible, some are very old fashioned" then carefully picked me a sensible one. But I guess from your perspective, the message is: read up on the risks, and talk to the consultant about what sort of options are available in terms of monitoring. (And Missus - I'd really ask for a second opinion - 37 weeks seems very early to insist on an induction).