???

The routing problem of internet nodes:

  the internet is not a physical space so tell me how do you
  measure distance between nodes?

To which you have no answer.

As stated in the OP:

  LN can't solve the TSP without either publishing a map of 
  all nodes and routes, or having all nodes broadcasts to all nodes. 

Unsurprisingly you didn't read the original post, nor contribute any response to the critique or technical implementation of routing in the LN design.

LN relies on hubs and a map. It's setup to extract wealth into centralized liquidity providers. This is antithetical to cash, and at this point why not use a faster centralized service like venmo?