Not sure about your figures. I just checked the DWP. The figures I found are HB of £75.85 per week (12% more than your figure) for social tenants, and £111.76 per week for private tenants (2.4% less than your figure). 68% of tenants claiming HB are in social housing.
The age group of 65+ accounts for 38% of HB recipients, and housing for this group is biased towards social housing rather than private rented. Since this age group has the lowest rent levels, it brings down the overall average for social housing compared to private rented, although of course the latter still costs more.
Nevertheless the average HB claim is £4,527 per annum.
If you include the average CTB claim, that ups this to £5205, on average.
If you include the JSA/Income Support, that ups this to £8,715 for an individual, or £10,714 for a couple, on average.
If you include child benefit and other kinds of welfare benefit, or look at tenants living in more expensive areas such as London, you quickly start the climb to £26k. Therefore it is possible to reach this cap of £26k, and there are numerous households that will reach it.
Unfortunately it is the minority of high earners and high achievers that are being forced to carry this burden.