Each added server cuts the average wait faster than one-over-N, because the extra capacity also pulls utilization away from the point where queues explode.

Waiting is governed less by raw capacity than by how close arrivals come to exhausting it. As utilization approaches one, the wait grows without bound; adding a server both raises the ceiling and moves the system back down the steep part of that curve.

The marginal server helps most when the system is already busy and barely helps when utilization is low, so the payoff of extra staff is largest exactly where queues are worst.

Faster service per server and more servers are interchangeable for raising capacity, but they are not interchangeable for wait time: many slow servers smooth variability better than one fast one.

Kleinrock, L. (1975). Queueing Systems, Volume 1: Theory. Wiley.