As you have noted, a lot of the literature on shift work and health focuses on rotating shift work, which is particularly harmful, since it puts the body into a state similar to permanent jet-lag. Meta-analyses (such as this one) have often grouped all types of night shift work together (rotating and permanent), making it difficult to distinguish their specific effects.
Currently there's very little good quality epidemiological work on fixed/permanent night shift work specifically. There's this meta-analysis, which suggests prostate cancer risk is specific to rotating schedules. There's also this recent study, which found that the increased risk of type 2 diabetes in shift workers did not extend to those on permanent night shift work. Note that survivorship bias can potentially play a role in these studies, because individuals who can 'survive' working permanent night shifts for long periods of time may be atypical, and in ways that are not easily adjusted for in statistical models.
Physiological studies of permanent night shift work show that very few individuals actually fully adjust the timing of their circadian rhythms to match their work schedule. This is largely because:
Light is the main factor that determines the timing of the human circadian system. It's difficult to adequately avoid exposure to natural light at times that will tend to undermine adaptation.
Many individuals who work consistent night shifts revert (partially or fully) to a different schedule on days off, as it allows for better social alignment with friends and family.
Lab studies have indicated that mismatch in internal vs. external timing is in general problematic to health for a number of reasons. Circadian clocks regulate metabolism, cognitive performance, quality of sleep, cardiovascular health, etc.