In the Military no enlisted man can tell an officer to take a watch or really to do anything unless so directed by an officer of higher rank then said officer.
In layman's terms

unless the Lt told me to assign Blake a watch shift I would not do so. Also Van you asked why I assigned Hatherford well there's only 6 grunts and the two officers, but if had been Moderate/Serious combat damage no I would not have assigned him a watch. I based it off Olan's last update of our state of health before the most recent as listed below. Taking into account Johannsen's serious cold damage at that time I gave her last watch with me giving her 4 hours of rest before her watch as the worst of the cold damage.
LT Kernan: mild cold damage.
PFC Pearson: moderate cold damage.
WO Blake: minimal cold damage, minimal combat damage.
CPL Hatherford: moderate cold damage, mild combat damage.
CPL Hart: moderate cold damage
SSG Kane: moderate cold damage
CPL Johannsen: serious cold damage
SGT Lee: mild cold damage