The Lightning Network design is exactly what the first sentence of Satoshi's Bitcoin whitepaper seeks to avoid - payment processor middlemen.
"A purely peer-to-peer version of electronic cash would
allow online payments to be sent directly from one party
to another without going through a financial institution." [2]
The LN design was chosen as a solution by certain investors who want to extract fees as payment hub liquidity providers.LN can't solve the TSP without either publishing a map of all nodes and routes, or having all nodes broadcasts to all nodes. The former significantly reduces decentralization and further removes the "electronic cash" aspect requiring payment processor hubs, while the latter will suffer from latency/scaling issues/DDoS susceptibility.
[1] https://en.wikipedia.org/wiki/Travelling_salesman_problem