The only risks I've heard about is one 20-year longitudinal study on prostate cancer (last update published in 2016.)
Evidence suggests that ejaculation frequency may be inversely related to the risk of prostate cancer (PCa), a disease for which few modifiable risk factors have been identified. [...]
The study includes 31,925 men who answered questions on ejaculation frequency on a 1992 questionnaire and followed through to 2010. [...] During 480,831 person-years, 3839 men were diagnosed with PCa. Ejaculation frequency at age 40–49 yr was positively associated with age-standardized body mass index, physical activity, divorce, history of sexually transmitted infections, and consumption of total calories and alcohol. Prostate-specific antigen (PSA) test utilization by 2008, number of PSA tests, and frequency of prostate biopsy were similar across frequency categories. In multivariable analyses, the hazard ratio for PCa incidence for ≥21 compared to 4–7 ejaculations per month was 0.81 (95% confidence interval [CI] 0.72–0.92; p < 0.0001 for trend) for frequency at age 20–29 yr and 0.78 (95% CI 0.69–0.89; p < 0.0001 for trend) for frequency at age 40–49 yr. Associations were driven by low-risk disease, were similar when restricted to a PSA-screened cohort, and were unlikely to be explained by competing causes of death.
The association was statistically significant, but a hazard ratio of around 0.8 probably isn't too concerning from a clinical perspective. On the other hand, this was a contrast between groups that had some ejaculation vs those that had frequent ones. It's hard to say how this might translate to those that have none. There were probably not enough real-life cases like that for them to include in that kind of study...
Aside: I double-checked elsewhere that 1 in 8 men indeed get diagnosed with prostate cancer in their lifetime. (I wasn't aware of that an the incidence in this study seemed pretty high.) Given that, a reduction in risk even by just a factor 0.8 is not insignificant from a public health perspective, but I suspect there isn't a whole lot the average man can do to increase their ejaculation rate by the 3x-5x as in that study... A more recent (2018) review flatly stated that
There is no evidence yet on how to prevent prostate cancer.
It does however have a section on ejaculatory frequency, which is mostly discussing the aforementioned study... which it characterizes as "weak evidence".