Lets start by looking at the level of risk. Roughly 5 serious brain injuries per million hours cycled, according the NZ data. For the UK roughly 300 million hours cycled per year would equate to 1500 brain injuries per year. if 10 million people use bicycles in the UK, that equates to one brain injury per 6000 years cycled or if cycling for 60 years per lifetime, once in 100 lifetimes.
So if a benefit occurs it would be unlikely to be in the average persons life of cycling.
Some research, Williams 1989 and Smith et al 1993, has detailed the impact location on helmets from typical accidents. It showed most were to the sides or temporal area of the head. Impacts to the top or front were less common, helmet testing may therefore be weak. Helmets usually reduce the levels of accelerations in testing but increase the duration of impacts, brain injury often depends on both.
Effects of bicycle helmet wearing on accident and injury rates, GB National Road Safety Conference, November 2019
https://www.researchgate.net/publicatio ... jury_rates
shows the accident rate increase with helmet use.
Robinson 1996 refers to the Wasserman data that detailed the incidence of cyclists hitting their head/helmet during an 18-month period was “significantly higher for helmet wearers (8/40 vs 13/476 - i.e. 20% vs 2.7%, p 0.00001)." A bare head width of approximately 150mm may avoid contact compared to a helmeted head at approximately 200mm wide (Clarke 2007). Assuming the 20% and 2.7% figures are typical, on a yearly average for helmeted and non-helmeted the risk of hitting their helmet or head would be 13.2% and 1.8% respectively. The increased risk of impact for helmeted about seven times higher. A degree of protection could be expected plus a degree of risk from the extra impacts.
Evaluating Cycling Fatality Risk with a Focus on Cycle Helmet Use Dec. 2018 http://worldtransportjournal.com/wp-con ... 4.4opt.pdf raises concerns.
http://nicochevalier.net/wp-content/upl ... iction.pdf
Colloids and Surfaces B: Biointerfaces
926 N.R. Chevalier / Colloids and Surfaces B: Biointerfaces 159 (2017) 924–928 ology willallowforhighthroughputmeasurementsofhair-on-hair friction
The static hair-on-hair friction coefficients I found were in the range 0.12–0.25; they are consistent with static (s) or dynamic (k) values reported in the literature (Schwartz et al. , s = 0.16–0.3 for wet hair; Sadaie et al.  k = 0.1 c–0.2 in air at 50% relative humidity (RH); Luengo et al.  k = 0.05–0.3 in air at 75% RH)
It appears the friction of human hair may be lower than for cycle helmets. Some research appears to be in error considering they are similar.
https://medcraveonline.com/MOJSM/biomec ... njury.html
Real-life accidents are rarely this simple, however, instead typically involving an oblique head impact 3 that produces a rotational torque on the helmet and thus, the head. Indeed, since angular brain acceleration can be more injurious than linear acceleration in impact scenarios,4 a helmet that can dissipate linear impact energy may either not sufficiently reduce, or may even increase, angular accelerations.
Defining the frictional coefficient between the human head and the impact surface required an appraisal of the literature; however, there is a wide range of skin friction values between μ = 0.5 and 1.1 25-27 although none describing interactions of the human scalp or hair,
Figure 8 Peak angular accelerations.
Shows from side impacts (quite a frequent impact zone), a higher peak angular acceleration. The friction coefficient of hair could be lower giving reduced levels of rotational accelerations.
The mean duration of PCS for helmet wearers was 22.9 months, and 16.8 months for patients not wearing a helmet at the time of concussion (p=0.41).
So it appears helmet wearers will incur more impacts and have bicycling-related concussions leading to longer periods - postconcussion syndrome in adults. In addition to more accidents.
So by not wearing a helmet you are more likely to gain a benefit in not having impacts and have a lower risk a concussion or multiple concussions and fewer accidents. This could mean you are protecting your brain by not wearing a helmet.
Some concussion data for the USA compared to cycling levels
Seems like more concussions compared with prior to widespread helmet use.
On the other hand some medical reports comparing helmeted to non-wearers find a lower proportion of head injuries for helmeted. They are usually comparing a relatively small sample of total accidents and falls.