the truth is, that NP-hardness is only true for perfect solution in polynomial time. good-enough solutions can be found in finite time intervals just fine, there are plenty of practical implementations of that.
ever heard of this thing called "delivery companies"? well they solve TSP sub-optimally millions of times every day.
shocker, i know.
Latency?
Let's look at the Lightening network white paper:
8.4 Payment Routing
It is theoretically possible to build a route map
implicitly from observing 2-of-2 multisigs on the
blockchain to build a routing table. Note, however, this
is not feasible with pay-to-script-hash transaction
outputs, which can be resolved out-of-band from the
bitcoin protocol via a third party routing service.
Building a routing table will become necessary for large
operators (e.g. BGP, Cjdns). Eventually, with
optimizations, the network will look a lot like the
correspondent banking network, or Tier-1 ISPs.
Why not just use venmo at that point?
Why would someone want to use Bitcoin with the LN, especially if it requires them buying Bitcoin from someone else?
The routing problem of internet nodes:
the internet is not a physical space so tell me how do you
measure distance between nodes?
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.
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?
You’re the one that claimed connection to TSP, you tell me.
Shortest path requires publishing all nodes and connections.
What if nodes go offline? How fast will the LN algorithm reroute? Does this mean everyone must connect to the Winkevoss/Bitmain/WellsFargo Nodes for payments?
Why would anyone bother dealing in Bitcoin when there's other usable alternatives, faster cryptocurrencies, or just paypal/venmo?