Thanks for the summary, Peter!
Zohar modeled the flow of coins as a random walk. For example, if a channel starts with Alice and Bob each holding $100 dollars, and if you imagine them routing through their channel N payments of $10 each, we'd expect the channel to be fully lopsided after routing 100 transactions ( [$100 / $10]^2 ).
It might actually be even worse than that if the transactions are not independent (and I assume they aren't, at least until the salary-in-BTC is a reasonable assumption).
If recharging the channel costs $30, then fees need to be at least $30 / 100 = $0.30 per transaction per hop. If it takes 5 hops to route your payment, that is at least $1.50 in fees.
However, increasing the number of channels per LN node makes the average unbalance converge to a normal (Gaussian) distribution: a bell centered on zero with a standard deviation (width) that grows with average transaction size.
The number of channels can be increased with limited (ideally null) additional financial exposure by making the channels smaller -
if the hypothetical transaction slicer/packetizer is in place.
Besides, you're assuming funding a channel costs 15% of the channel capacity (30$ for 200$ capacity). I don't think this is realistic, as the blockchain related funding cost should only be a function of the number of utxos under SW regime.
And it would definitely be a SW transaction.
I guess we'll see.
