I don't know any doctors who still tell women that about heart rate.
You are misinformed if you think that ultrasound results won't change treatment for the mother or the baby. They can and do. The things in green can not necessarily be confirmed by other methods. Those other methods are limited in what they can tell us.
Knowing there is something wrong with the placenta can influence our care of a laboring women immensely. Placenta previa is the most obvious example. If you don't know you have it and try to give birth vaginally, there is a good chance you'll bleed to death (this is also one of the possible reasons for bleeding in pregnancy). Aside from the physical benefits, the emotional benefits are immense. Sure parents survive even when they are surprised by a congenital defect the day their baby is born, but they don't do as well as parents who are prepared ahead of time. And yes, a lot of parents will decide whether or not to terminate pregnancies based on ultrasound results. There are conditions for which I would choose that. You may not see that as a benefit, but it is for lots of people. I wouldn't want to carry an anecephalic baby to term just to watch it die. Being spared that because of an ultrasound would be a positive for me.
It also isn't so simple at birth for the baby. Certain defects need treatment immediately or they will result in serious injury or death. Give birth to a baby with hypoplastic left heart or tetralogy of Fallot or a congenital diaphragmatic hearnia in a small hospital without specialists and your chance of a good outcome decrease significantly. Those babies usually need immediate treatment. Part of the treatment we routinely do at delivery can be harmful for cardiac patients. In duct dependent conditions, the baby NEEDS a duct called the ductus arteriosis to stay open in order to survive. If we don't know that and give the baby oxygen because it seems stressed we can actually cause it to close.
I do know doctors that tell women about the relationship between heart rate and fetal gender - that's where I learned it ... from two different doctors that looked after my pregnancies. It fell into the realm of an old wives tale after ultrasound results compared heart rate and gender, but there is no reason to assume that the ultrasound doesn't stress the fetus and cause the heart rate to be different than a restful state.
Regardless of the specific abnormalities in newborns, it still doesn't justify subjecting thousands of unborn babies to unnecessary, medically intrusive, procedures. Deep ultrasound, replacing the amnio, is even more intrusive and even more unnecessary for 98% of pregnancies. Keep these procedures as optional but don't treat pregnant women as having an illness ... because they are not sick people, they are pregnant - a perfectly healthy and normal part of a woman's life.