That was the big "sky is falling" issue when BasicMed was just an idea. I pooh-poohed it.
According to the most recent FAA study (2021). While it disclaims ultimate generalizations due to the sample sizes (your "time will tell")
The estimated overall accident rate per 100,000 flight hours for the BasicMed group was 7.3 (fatal: 1.6) compared to 7.0 (fatal: 1.4) for the medically certified pilots. The fatal accident rate per 100,000 flight hours was 1.6 for the BasicMed group and 1.4 for the medically certified pilots. The differences in overall and fatal accidents were not statistically significant. No statistically significant differences were found when multiple age subgroups were compared. Also, logistic regression models adjusted for relevant confounders revealed no significantly elevated accident ORs between the BasicMed and third-class certified pilot groups overall.
And that doesn't account for whether the cause of the accidents was a medical deficiency. On that score, there's the 2022 FAA Safety Briefing,
Medical Factors in Aviation Mishaps where Dr Northrup suggests drugs, alcohol, and unreported medical conditions were involved in a statistically significant number of fatal accidents:
Over 40% had incidental medical findings (IMFs), which are medical conditions not previously known by the FAA, but discovered on autopsy. The NTSB determined that for this group of pilots, the most common medical issues, that were either causal or contributory, were use of a sedating medication, followed by alcohol or illicit drug use, cardiovascular disease, neuropsychiatric problems, and strokes.
I'm really bad at statistical analysis but in my mind, the two puts drugs, alcohol, and flying with a known deficiency, all of which can and do take place with Class 1, 2 and 3 medical certificate holders as well as BasicMed pilots, way ahead of any BasicMed-related issues.