NHTSA's power is simultaneously very broad and narrow. They're empowered to investigate potential safety issues after the fact, but this may not be a safety issue in the very pedantic sense often used. NHTSA can proactively set standards, but the standards they've set (FMVSS) largely ignore modern electronics. So on and so forth.
NHTSA has been involved in recalls of OTAs that involve safety issues in the past, sometimes for things more minor than this, as long as it is something that affects safety equipment. e.g. stereo recalls because the backup camera took too long to display when shifted into reverse.
