That might seem to be the case at first glance, but three things go against such an idea:
First, such a recommendation would do nothing to lessen the "patient load" of the National Health Service. Maybe you read the link too quickly, because the recommendation is not simply that "more women give birth at home", but that "more women give birth at home
with the help of a midwife." Midwives are paid for by the National Health Service.
Second, the Royal College of Obstetricians and Gynaecologists is a professional body, and makes all sorts of recommendations regarding obstetrics and gynaecology, but does not "hold the purse strings" of the National Health Service. If you go to the
news page of its web site, you will see that most of its recommendations have implications of cost increase.
Thirdly, your view seems to ignore the fact that there would be
increased costs involved if health professionals were to be sent out to individual homes for births. There would be extra time and fuel costs in travelling (and remember, petrol/gas is much more expensive here than in America). Then there would need to be more midwives available, each with the necessary medical training, and equipment.
No, it is not a money-saving idea.