No, dedicated servers do not have lower latency than a direct connection.

You don't make packets go faster by putting something else in the middle. That's how they go slower.
So, I'm obviously subtweeting That Game but real talk from network guy:

You cannot remove latency. It's there, it's a fact of life. You can hide it, you can perform trickery to compensate for it, but, ultimately, it's smoke and mirrors. Time doesn't disappear.
There's two parts to networking in a game: The clock synchronization and the game state synchronization. Both matter, especially for lockstep games.
Clock sync is how you get your game running smooth.

Game state sync is how you keep the games accurate on both players sides.

The reason there's such variance in netcode is that there's a lot of approaches to both. (And many rollback implementations fail the clock side, too!)
In most rollback implementations, both players are authoritative and depend on each other to stay in sync.

Dedicated server, as a concept, essentially adds another player to the mix, saying this one player is authoritative.
It's the Parsec problem all over again: It's 'great' for people in a small region, but at distance, the latency balloons up beyond traditional methods, because it _must_ be round trip, and is often one-sided, because geography isn't evenly split between two players.
Dedicated servers are advantageous for >1v1 games because keeping that many players in sync is impractical at the best of times, comically impossible at the worst.

But even then, we know how much your ping to the server gives you an advantage, from other competitive games.
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