The blog author and you need to learn about lighting network and graph theory.

Edit: responses to the specific "proof" you linked

https://medium.com/@murchandamus/i-have-just-read-jonald-fyo...

https://medium.com/@murchandamus/some-subsidiary-points-on-l...

That's just a lot of hand-waving, if the author is so confident about his rebuttal he should be able to provide a model for it. This person did at least attempt to simulate something along the lines of an ideal LN, which showed that micropayments do not do very well at all due to the combination of fees accrued at each hop:

https://hackernoon.com/simulating-a-decentralized-lightning-...

This thread on the same story discusses other issues with LN proposals, one that stands out to me is how routing is going to work if all nodes are perfectly equal - routing on the internet relies on a hub model, seems likely that a decentralised routing protocol adds even more complexity and resource requirements.

https://news.ycombinator.com/item?id=14759965

The trouble of course is that LN is just a bunch of proposals right now, each promising to fix all of Bitcoin's issues without removing all of its unique features. When it actually exists then I'll revisit, but until then I'll treat it as another piece of vapourware.

> The trouble of course is that LN is just a bunch of proposals right now,

There are multiple implementations of the spec.