Both René's distribution of channel balances and your beta distribution are making lots of assumptions about the actual liquidity placement in the network and "who wants to pay who".
That's fair. I would say Rene's assumption is as nonbiased as possible. I add a little intuition with mine because I have to pick alpha and beta out of thin air. The results are important to mention because the beta distribution is so expressive. You could describe funding behavior between nodes at the network level, node level, or the node pair level when taking balance samples.
On some level, who cares if I can't pay some node I was never going to pay anyways? Maybe the amateur nodes aren't actually getting worse at payment reliability? Perhaps they are just optimized for paying hub nodes rather than paying one another.
IMO the most important outcome of the work are the network level SLAs. I think breaking down which connections contribute to that SLA would give insight as to which nodes are actual 'liquidity service providers' of the network. Once again, you could go down to the node level, or the node pair level.