> If all hops are connected to the same LSP, I don't think this adds any privacy

If you yourself run rack proxy software, it would add privacy for you and for anyone who routes through you, for two reasons: (1) even if everyone *was* using the same LSP, the LSP has no way of knowing that (2) the LSP can no longer safely assume the payments you receive are actually yours -- you could just be routing them to some other destination, since the rack server software makes you a routing node, and the LSP does not know what other channels you might have, through which you route these payments to others

> All hops will route through the same LSP

There's no reason to expect different proxies to use the same LSP. The list of LSPs I recommended has 10 different LSPs plus another LSP aggregator -- liquiditystr -- which currently has 4 additional LSPs besides the ones on my list. Moreover, using an LSP is only a recommendation -- you can also just start opening up channels to popular destinations or other routing nodes, as long as you get yourself some inbound capacity somehow (e.g. by paying someone).