I'm not sure where the comparision between battlefield mortality and childbirth-related mortality came from (well, there's Euripides' Medea: 'I would rather stand three times in the line of battle than bear a single child') but I am finding it odd that the modern mortality rate related to expectant and new mothers [new-born infants haven't been mentioned, I think], including Black women, turns out to be low relative to... men going out and getting killed in war, where one crucial aim is to, you know, kill as many of the other side as possible (or render them unable to fight back).
No-one will deny that war has always taken its highest toll on young men. The casualty numbers in WW1 in particular are terrifying. But we have to consider that, until comparatively recently, conscription wasn't a Thing. Centralized control over nation-states of a kind to make conscription possible wasn't even achieved until the mid-late 19th c.; a state has to be equipped with a massive bureaucracy and a police service or standing army to enforce its rules easily in order to build a conscript army. The changes (massive industrialization imprimis) that transformed wars into wars of technology and GDP both exploited and helped create ever-increasing bureaucratization (and eventually the Hollerith Company's [i.e. IBM] punch-card system made it possible for the Nazis to identify, locate, and round up Jews and other "undesirables" easily).
For centuries before that, in contrast, military service was largely a choice (with exceptions, I know: press-gangs etc.). If service was expected, it was often accepted gladly, as appropriate to one's status (those upper-class young men going into the Guards); even earlier it already came with one's social position (e.g. feudal responsibilities to fight or provide soliders for one's lord). Nowadays the US armed forces have to outsource so much to what are basically mercenaries in part precisely because it's a volunteer service, and the last time conscription was used it didn't go so well. And mortality is so low compared to, say, the Civil War because of advances in battle-field care and in subsequent medical care—medical care that doesn't necessarily extend to pregnant women: There is no doubt that in the US at least Black and other minority women receive less and less good ante- and post-natal care than do whites and Asian-origin women:
www.ywboston.org/wp-content/uploads/2016/02/FACT_SHEET_MATERNAL_HEALTH_AND_WOMEN_
There are plenty of female soldiers, sailors, and airforce personnel now, of course, who have had a fight on their hands to be allowed to go into battle; but the history of warfare is peppered by their presence, usually in support rôles—not just cooking and cleaning for them (and the children who also had a place in the "baggage train"), but bringing the ammunition to the guns, cleaning weapons, and often, especially after medium- and long-range artillery became common, running much the same risks as the soldiers and sailors they assisted. Unlike their Russian counterparts, women pilots in the UK were allowed only to move aircraft between airfields; they weren't "safe" by choice. Women in the UK in WW1 and WW2 volunteered or were conscripted to work in steelyards and armament factories, doing the same jobs as men, for less pay, even during the Blitz... and then got chucked out as soon as the men came home.
Childbirth, of course, has never been a choice for women (with the tiniest of exceptions for Serbian sworn virgins, Roman Vestal Virgins, etc.). It still isn't, for millions of women around the world. From the WHO:
'The World Health Organization estimates that more than 300,000 women died from pregnancy-related causes in 2015 [This is down from over 500k in 1990.]. That’s 830 women every day.
'In the chart here we see global maternal deaths by region. Two-thirds – 201,000 – occurred in Sub-Saharan Africa. 22% – 66,000 – occurred in South Asia.
'This is partly attributed to the fact that many more babies are born in Asia and Africa than in other regions. But it is also largely the result of the much higher maternal mortality rates found in lower-income countries. Per birth, a woman in Nigeria is more than 200 times more likely to die in pregnancy or childbirth than a woman in Sweden.''